Abstract: Reachability analysis provides formal guarantees for performance and safety properties of nonlinear control systems. Here, one aims to compute the backward reachable set (BRS) or tube (BRT)—the set of states from which the system can be driven into a target set at a particular time or within a time interval, respectively. The computational complexity of current approaches scales poorly, making application to high-dimensional systems intractable. We propose a technique that decomposes the dynamics of a general class of nonlinear systems into subsystems which may be coupled through common states, controls, and disturbances. Despite this coupling, BRSs and BRTs can be computed efficiently using our technique without incurring additional approximation errors and without the need for linearizing dynamics or approximating sets as polytopes. Computations of BRSs and BRTs now become orders of magnitude faster, and for the first time BRSs and BRTs for many high-dimensional nonlinear control systems can be computed using the Hamilton–Jacobi formulation. In situations involving bounded adversarial disturbances, our proposed method can obtain slightly conservative results. We demonstrate our theory by numerically computing BRSs and BRTs for several systems, including the six-dimensional Acrobatic Quadrotor using the HJ formulation.

Abstract: This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.

Abstract: A distributed nonlinear controller is presented to achieve both accurate current-sharing and voltage regulation simultaneously in dc microgrids (MGs) considering different line impedances effects among converters. Then, an improved event-triggered principle for the controller is introduced through combining the state-dependent tolerance with a nonnegative offset. In order to design the event-triggered principle and guarantee the global stability, a generalized dc MG model is proposed and proven to be positive definite, based on which Lyapunov-based approach is applied. Furthermore, considering the effects from constant power loads, the damping performance of proposed controller is further improved which is comparative with the traditional $V\hbox{--}I$ droop controller. The proposed event-triggered-based communication strategy can considerably reduce the communication traffic and significantly relax the requirement for precise real-time information transmission, without sacrificing system performance. Experimental results obtained from a dc MG setup show the robustness of the new proposal under normal, communication failure and communication delay operation conditions. Finally, communication traffic under different communication strategies is compared, showing a drastic traffic reduction when using the proposed approach.

Abstract: This paper presents the development of an adaptive neural controller for a class of nonlinear systems with unmodeled dynamics and immeasurable states. An observer is designed to estimate system states. The structure consistency of virtual control signals and the variable partition technique are combined to overcome the difficulties appearing in a nonlower triangular form. An adaptive neural output-feedback controller is developed based on the backstepping technique and the universal approximation property of the radial basis function (RBF) neural networks. By using the Lyapunov stability analysis, the semiglobally and uniformly ultimate boundedness of all signals within the closed-loop system is guaranteed. The simulation results show that the controlled system converges quickly, and all the signals are bounded. This paper is novel at least in the two aspects: 1) an output-feedback control strategy is developed for a class of nonlower triangular nonlinear systems with unmodeled dynamics and 2) the nonlinear disturbances and their bounds are the functions of all states, which is in a more general form than existing results.

Abstract: This note investigates the problem of global output feedback stabilization for a class of nonlinear systems with unknown measurement sensitivity. A new design method, namely dual-domination approach , is proposed to explicitly construct a state observer as well as an output feedback control law, which globally asymptotically stabilizes the nonlinear systems. The novelty of this note owes to a distinct perspective in coping with unknown measurement sensitivity which has previously been a hurdle to solve the global output feedback stabilization problem of the nonlinear systems.

Abstract: Modular multilevel converters (MMCs) are multi-input multi-output (MIMO) nonlinear systems. The control systems for MMCs are required to simultaneously achieve multiple control objectives, e.g., output current regulation, submodule capacitor voltage control, and circulating ripple currents suppression. Existing cascaded control strategies for MMCs achieve those control objectives with relatively complex controllers, and the controller parameter design is normally difficult for such nonlinear systems with highly coupled states. In view of this, a feedback linearization-based current control strategy is proposed for an MMC system in this paper. The nonlinear state function model of the MMC is presented and transformed to a linearized and decoupled form with the help of the input–output feedback linearization technique. Based on the linearized system, simple linear controllers are employed to regulate the output and inner differential currents of the MMC, which significantly reduces the difficulty in controller design. The stability of the proposed control strategy is analyzed. The experimental verification results show that, compared to the conventional cascaded control strategies for MMCs, the proposed feedback linearization control strategy is able to achieve improved steady-state and dynamic performances. The robustness of the proposed control strategy against parametric uncertainties is experimentally investigated.

Abstract: This paper presents an analog-assisted (AA) output-capacitor-free digital low-dropout (D-LDO) regulator with tri-loop control. For responding to instant load transients, the proposed high-pass AA loop momentarily adjusts the unit current of the power switch array, and significantly reduces the voltage spikes. In the proposed D-LDO, the overall 512 output current steps are divided into three sub-sections controlled by coarse/fine loops with carry-in/out operations. Therefore, the required shift register (SR) length is reduced, and a 9-bit output current resolution is realized by using only 28-SR bits. Besides, the coarse-tuning loop helps to reduce the recovery time, while the fine-tuning loop improves the output accuracy. To eliminate the limit cycle oscillation and reduce the quiescent current, a freeze mode is added after the fine-tuning operation. To reduce the output glitches and the recovery time, a nonlinear coarse word control is designed for the carry-in/out operations. The D-LDO is fabricated in a 65-nm general purpose CMOS process. A maximum voltage undershoot/overshoot of 105 mV is measured with a 10-mA/1-ns load step and a total capacitor of only 100 pF. Thus, the resulting figure-of-merit is 0.23 ps.

Abstract: In this paper, an adaptive fuzzy predictive controller (AFPC) is designed and analyzed for a class of networked nonlinear systems with time-varying communication delay. The integration of the communication network in the control loops makes the nonlinear system has forward and feedback time-varying delays. The proposed controller compensates the network-induced delays in the forward and feedback channels. The structure of the AFPC consists of adaptive fuzzy logic control (AFLC) with state predictor located at the controlled plant and a remote adaptive smith predictive controller at the master node. The AFLC and the state predictor are utilized to identify the dynamic of the time-varying delay-free nonlinear plant in order to cancel the nonlinear term for the nonlinear control system in a canonical form. In the remote controller, adaptive smith predictor is employed to compensate the time-varying delay effect to achieve the desired tracking performance. Based on the Lyapunov theory, the stability of the closed-loop system is guaranteed in the presence of bounded external disturbance and time-varying delays. Simulated application of Van der Pol oscillator is provided to demonstrate the feasibility and effectiveness of the proposed scheme based on TrueTime toolbox.

Abstract: This study explores the stabilization problem of nonlinear systems subject to parameter uncertainties, time-varying delay, and data-packet dropouts. An interval type-2 Takagi-Sugenofuzzy model is employed to represent nonlinear systems subject to parameter uncertainties. The lower and upper membership functions of the system enable parameter uncertainties to be captured effectively. To enhance the flexibility of design, the proposed state feedback controller does not share the premise membership functions of the model. Unlike the majority of existing results, the present study simultaneously considers parameter uncertainties, time-varying delay, and data-packet dropouts in nonlinear control systems. A novel finite-sum inequality that includes well-known inequalities as special cases, is developed to derive new stability conditions in the form of linear matrix inequalities. Several examples of simulation are used to demonstrate the effectiveness of the proposed approach.

Abstract: Existing control schemes for single-phase ac-to-dc converters with active power-decoupling function typically involve a dedicated power-decoupling controller. Due to the highly coupled and nonlinear nature of the single-phase system, the design of the power-decoupling controller (typically based on the small-signal linear control techniques) is cumbersome, and the control structure is complicated. Additionally, with the existing power-decoupling control, it is hard to achieve satisfied dynamic responses and robust circuit operation. Following a recently proposed automatic-power-decoupling control scheme, this paper proposes a nonlinear control method that can achieve enhanced large-signal dynamic responses with strong disturbance rejection capability without the need for a dedicated power-decoupling controller. The proposed controller has a simple structure, of which the design is straightforward. The control method can be easily extended to other single-phase ac-to-dc systems with active power-decoupling function. Simulation and experimental results validate the feasibility of the proposed control method on a two-switch buck–boost PFC rectifier prototype.

Abstract: Traditionally, the vector operation technique (VOT) has been used to control three-phase converters using one cycle control. In this paper, a three-phase active power filter large-signal model with a VOT in a new coordinate system is presented. By using the VOT, only two phase-legs are switching at high frequency, thus reducing the switching losses. This paper not only covers the literature gap about the modeling of three-phase converters using the vector operation, but also presents a sliding mode control for this converter. The control scheme consists of a nonlinear matrix transformation in order to obtain the voltages and currents in a new two-dimensional frame, $\gamma \theta$ -frame, a sliding mode controller designed in these coordinates, and a modulator to obtain the control signals in a natural frame. The sliding mode control is designed with the help of the presented large-signal model assuring sinusoidal grid currents in phase with the grid voltages. This controller provides a fast transient response against sudden load changes with a good current tracking capability and a reduction of the switching losses. A stability analysis is performed in order to validate the control parameters. Experimental results are provided using a fully digital control system in order to validate the performances of the proposed controller.

Abstract: In this paper, we propose a compositional scheme for the construction of abstractions for networks of control systems by using the interconnection matrix and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a control system (possibly with a lower dimension), can be used as a substitution of the original system in the controller design process. Moreover, we provide a procedure for constructing abstractions of a class of nonlinear control systems by using the bounds on the slope of system nonlinearities. We illustrate the proposed results on a network of linear control systems by constructing its abstraction in a compositional way without requiring any condition on the number or gains of the subsystems. We use the abstraction as a substitute to synthesize a controller enforcing a certain linear temporal logic specification. This example particularly elucidates the effectiveness of dissipativity-type compositional reasoning for large-scale systems.

Abstract: LLC resonant converter is a nonlinear system, limiting the use of typical linear control methods. This paper proposed a new nonlinear control strategy, using load feedback linearization for an LLC resonant converter. Compared with the conventional PI controllers, the proposed feedback linearized control strategy can achieve better performance with elimination of the nonlinear characteristics. The LLC resonant converter's dynamic model is built based on fundamental harmonic approximation using extended describing function. By assuming the dynamics of resonant network is much faster than the output voltage and controller, the LLC resonant converter's model is simplified from seven-order state equations to two-order ones. Then, the feedback linearized control strategy is presented. A double loop PI controller is designed to regulate the modulation voltage. The switching frequency can be calculated as a function of the load, input voltage, and modulation voltage. Finally, a 200 W laboratory prototype is built to verify the proposed control scheme. The settling time of the LLC resonant converter is reduced from 38.8 to 20.4 ms under the positive load step using the proposed controller. Experimental results prove the superiority of the proposed feedback linearized controller over the conventional PI controller.

Abstract: In this paper, a robust inertia-free attitude takeover control scheme with guaranteed prescribed performance is investigated for postcapture combined spacecraft with consideration of unmeasurable states, unknown inertial property and external disturbance torque. Firstly, to estimate the unavailable angular velocity of combination accurately, a novel finite-time-convergent tracking differentiator is developed with a quite computationally achievable structure free from the unknown nonlinear dynamics of combined spacecraft. Then, a robust inertia-free prescribed performance control scheme is proposed, wherein, the transient and steady-state performance of combined spacecraft is first quantitatively studied by stabilizing the filtered attitude tracking errors. Compared with the existing works, the prominent advantage is that no parameter identifications and no neural or fuzzy nonlinear approximations are needed, which decreases the complexity of robust controller design dramatically. Moreover, the prescribed performance of combined spacecraft is guaranteed a priori without resorting to repeated regulations of the controller parameters. Finally, four illustrative examples are employed to validate the effectiveness of the proposed control scheme and tracking differentiator.

Abstract: Offshore cranes often work in harsh sea conditions. As a result, they may suffer from various external disturbances, especially the persistent and unpredictable ship motion caused by sea waves, which will introduce severe disturbances to the crane dynamics, including the unactuated part. Due to this reason, the control problem for offshore boom cranes presents great challenges, for which only boundedness or stability, instead of the generally desired asymptotic stability, of the closed-loop system can be usually guaranteed by currently available methods. For this problem, a novel nonlinear control strategy for an offshore crane is proposed in this brief, which ensures that the closed-loop system’s equilibrium point is asymptotically stable even in the presence of the persistent ship roll disturbances. The proposed control law is further extended to be an output feedback controller to deal with the situations when the velocities are unavailable, still guaranteeing asymptotic stability. Finally, some experimental results are provided to validate the efficiency of the proposed controllers.

Abstract: This paper presents an optimal and robust nonlinear control scheme to achieve trajectory tracking for disturbed nonlinear systems, which is applied for the control of power converters in dc microgrids. The state-feedback optimal controller synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation, which considers the minimization of a cost functional (performance index), resulting in an efficient control strategy. The proposed methodology is used to efficiently regulate the power flow from renewable resources into the utility grid, to supply energy to loads, and to storage energy. Simulation results are presented to assess the performance of the proposed controller for a case study dc microgrid, where its adequate operation depends on the dc bus voltage regulation; hence, for guaranteeing such voltage regulation through the converter (inverter) connected to the utility grid, the optimal control scheme is in addition combined with a super-twisting controller (a robust sliding mode-based control technique) to enhance the inverter control strategy robustness.

Abstract: This paper investigates the output consensus problem of heterogeneous stochastic nonlinear multiagent systems with directed communication topologies, with a view of making the outputs of a group of follower agents track the output of a leader Fuzzy logic systems are applied to approximate the unknown nonlinear functions of agents A special case that all followers can get access to the leader is first considered, and a novel decentralized adaptive fuzzy control law based on the output regulation framework is presented Next, the proposed control scheme is further applied to design the distributed adaptive fuzzy control law for a more general case that only part of agents can get access to the leader By applying Lyapunov stability analysis, it is shown that the outputs of followers will achieve consensus to a sufficient small bound of the output of the leader under the proposed control law Finally, simulation results demonstrate that the proposed control law is effective and efficient The developed distributed control scheme can be widely applied to solve the cooperative control problem of practical autonomous systems with uncertain dynamics such as synchronization of mechanical systems with vibration, formation control of autonomous underwater vehicles, etc

Abstract: The tracking control of a quadrotor has been considered in this paper. The application of sliding mode control provides robustness against parametric uncertainties, but it requires knowledge of the...

Abstract: This article addresses the design and implementation of robust nonlinear control approaches to obtain the desired trajectory tracking of a flexible joint manipulator driven with a direct-current (DC) geared motor. The nonlinear control schemes have been designed and implemented such that they locally stabilize the closed loop system considering all the states as bounded. The system model has been derived using Euler-Lagrange approach. Two different approaches based on sliding mode control (SMC), i.e. the traditional SMC and integral SMC, have been considered in the present study. To experimentally validate the proposed control laws, an electrically-driven single-link flexible manipulator has been designed and fabricated. The designed control algorithms have been developed and experimentally validated on the custom-developed platform. The results obtained both from MATLAB/Simulink and the experimental platform verify the performance of the proposed control algorithms.

Abstract: This paper presents a robust adaptive integral backstepping control strategy with friction compensation for realizing accurate and stable control of opto-electronic tracking system in the presence of nonlinear friction and external disturbance. With the help of integral control term to decrease the steady-state error of the system and combining robust adaptive control approach with the backstepping design method, a novel control method is constructed. Nonlinear modified LuGre observer is designed to estimate friction behavior. Robust adaptive integral backstepping control strategy is developed to compensate the changes in friction behavior and external disturbance of the servo system. The stability of the opto-electronic tracking system is proved by Lyapunov criterion. The performance of robust adaptive integral backstepping controller is verified by the opto-electronic tracking system with modified LuGre model in simulation and practical experiments. Compared to the adaptive integral backstepping sliding mode control method, the root mean square of angle error is reduced by 26.6% when the proposed control method is used. The experiment results demonstrate the effectiveness and robustness of the proposed strategy.

Abstract: Rapidly depleting oil and natural gas resources, global warming issue, and depletion of fossil fuels are motivating the development of alternative technology for vehicular systems. Thus, an increasing number of studies have been conducted on fuel cell electric vehicles (FCEVs). This paper proposes a modeling and nonlinear control for hybrid energy storage system (HESS) in FCEVs. HESS consists of fuel cell (FC) as the main source and battery and ultracapacitor (UC) as secondary sources. Each source is connected to DC bus via DC–DC converter: FC is connected to DC bus via boost converter, while battery and UC are connected to DC bus via buck–boost converter. Based on the nonlinear behavior of power sources and converters, a dynamic model of the system is developed. A nonlinear control technique based on Lyapunov theory is applied to meet the following requirements: (1) accurate DC bus voltage regulation and (2) rapid tracking of battery and UC current to their desired reference values. Both mathematical analysis and simulations are performed to prove the asymptotic convergence of the proposed controller. To verify the performance of the controller, simulations have been done on MATLAB/Simulink, which show that the proposed controller ensures the stability of closed loop system and meet all the control objectives.

Abstract: In this paper, we provide a systematic approach for the design of stabilizing feedback controllers for nonlinear control systems using the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this paper is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Simulation results are presented to verify the main results on the design of stabilizing feedback controllers and the data-driven aspect of the proposed approach.