Abstract: In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.

Abstract: In this paper, an output feedback nonlinear control is proposed for a hydraulic system with mismatched modeling uncertainties in which an extended state observer (ESO) and a nonlinear robust controller are synthesized via the backstepping method. The ESO is designed to estimate not only the unmeasured system states but also the modeling uncertainties. The nonlinear robust controller is designed to stabilize the closed-loop system. The proposed controller accounts for not only the nonlinearities (e.g., nonlinear flow features of servovalve), but also the modeling uncertainties (e.g., parameter derivations and unmodeled dynamics). Furthermore, the controller theoretically guarantees a prescribed tracking transient performance and final tracking accuracy, while achieving asymptotic tracking performance in the absence of time-varying uncertainties, which is very important for high-accuracy tracking control of hydraulic servo systems. Extensive comparative experimental results are obtained to verify the high-performance nature of the proposed control strategy.

Abstract: Because of the complicity of consensus control of nonlinear multiagent systems in state time-delay, most of previous works focused only on linear systems with input time-delay. An adaptive neural network (NN) consensus control method for a class of nonlinear multiagent systems with state time-delay is proposed in this paper. The approximation property of radial basis function neural networks (RBFNNs) is used to neutralize the uncertain nonlinear dynamics in agents. An appropriate Lyapunov–Krasovskii functional, which is obtained from the derivative of an appropriate Lyapunov function, is used to compensate the uncertainties of unknown time delays. It is proved that our proposed approach guarantees the convergence on the basis of Lyapunov stability theory. The simulation results of a nonlinear multiagent time-delay system and a multiple collaborative manipulators system show the effectiveness of the proposed consensus control algorithm.

Abstract: This paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models-systems with impulse effects-through control Lyapunov functions. The periodic orbit is assumed to lie in a C1 submanifold Z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics; the associated restriction dynamics are termed the hybrid zero dynamics. The orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics. Prior results on the stabilization of such periodic orbits with respect to the full-order dynamics of the system with impulse effects have relied on input-output linearization of the dynamics transverse to the zero dynamics manifold. The principal result of this paper demonstrates that a variant of control Lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface, Z, can be used to achieve exponential stability of the periodic orbit in the full-order dynamics, thereby significantly extending the class of stabilizing controllers. The main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control Lyapunov functions.

Abstract: This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.

Abstract: We consider a class of linear dynamical systems containing uncertain elements and subject to uncertain inputs, and for which either uncertain state or output is available. We construct a feedback control, utilizing measured state or estimated state, which guarantees that every system response is ultimately bounded within a certain neighborhood of the zero state. Performance resulting from use of this control is compared with that due to the use of purely linear feedback control.

Abstract: This study is concerned with the event-triggered control for networked control systems via dynamic output feedback controllers (DOFCs). The output measurement signals of the physical plant are sampled periodically. An output-based discrete event-triggering mechanism is introduced to choose those only necessary sampled-data packets to be transmitted through a communication network for controller design. Under this event-triggering mechanism, the resultant closed-loop system is first modelled as a linear system with an interval time-varying delay. Then a novel stability criterion is established by employing the Lyapunov-Krasovskii functional approach. Based on this stability criterion, a new sufficient condition is derived to co-design both the desired DOFCs and the event-triggering parameters. Finally, a satellite control system is taken to show the effectiveness of the proposed method.

Abstract: A method to synchronize and control a system of parallel single-phase inverters without communication is presented. Inspired by the phenomenon of synchronization in networks of coupled oscillators, we propose that each inverter be controlled to emulate the dynamics of a nonlinear dead-zone oscillator. As a consequence of the electrical coupling between inverters, they synchronize and share the load in proportion to their ratings. We outline a sufficient condition for global asymptotic synchronization and formulate a methodology for controller design such that the inverter terminal voltages oscillate at the desired frequency, and the load voltage is maintained within prescribed bounds. We also introduce a technique to facilitate the seamless addition of inverters controlled with the proposed approach into an energized system. Experimental results for a system of three inverters demonstrate power sharing in proportion to power ratings for both linear and nonlinear loads.

Abstract: This paper proposes a combined system of a thyristor-controlled reactor (TCR) and a shunt hybrid power filter (SHPF) for harmonic and reactive power compensation. The SHPF is the combination of a small-rating active power filter (APF) and a fifth-harmonic-tuned LC passive filter. The tuned passive filter and the TCR form a shunt passive filter (SPF) to compensate reactive power. The small-rating APF is used to improve the filtering characteristics of SPF and to suppress the possibility of resonance between the SPF and line inductances. A proportional-integral controller was used, and a triggering alpha was extracted using a lookup table to control the TCR. A nonlinear control of APF was developed for current tracking and voltage regulation. The latter is based on a decoupled control strategy, which considers that the controlled system may be divided into an inner fast loop and an outer slow one. Thus, an exact linearization control was applied to the inner loop, and a nonlinear feedback control law was used for the outer voltage loop. Integral compensators were added in both current and voltage loops in order to eliminate the steady-state errors due to system parameter uncertainty. The simulation and experimental results are found to be quite satisfactory to mitigate harmonic distortions and reactive power compensation.

Abstract: In this paper, an adaptive fuzzy robust output feedback control problem is considered for a class of single-input and single-output nonlinear systems in a strict-feedback form. The considered systems possess the unstructured uncertainties, unknown dead zone, and the dynamics uncertainties, and they do not assume the states being available for the controller design. In the controller design, fuzzy logic systems are first used to approximate the unstructured uncertainties, and by utilizing the information of the bounds of the dead-zone slopes and treating the time-varying inputs coefficients as a system uncertainty, a fuzzy state observer is designed to estimate the unmeasured states. By combining a backstepping technique with a nonlinear small-gain approach, a new adaptive fuzzy robust output feedback control has been developed. It is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed-loop systems. Simulation studies and comparisons with previous methods are included to illustrate the effectiveness of the proposed approach.

Abstract: This paper considers the problem of finite-time synchronization for a class of second-order nonlinear multi-agent systems with a leader-follower architecture. By using the finite-time control technique and homogenous systems theory, a finite-time state feedback controller is first proposed. Then to address the lack of velocity measurement, a finite-time convergent observer is constructed to estimate the unknown velocity information in a finite time. Finally, an observer-based finite-time output feedback controller is developed. Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leader's states. In addition, for some special second-order multi-agent systems, a bounded finite-time output feedback controller can also be designed.

Abstract: This paper is concerned with active control for an offshore steel jacket platform subjected to wave-induced force and parameter perturbations. An uncertain dynamic model for the offshore platform is first established, where uncertainties not only on the natural frequency and the damping ratio of both the offshore platform and the active tuned mass damper (TMD) but also on the damping and stiffness of the TMD are considered. Then, by intentionally introducing a proper time delay into the control channel, a novel sliding mode control scheme is proposed. This scheme uses information about mixed current and delayed states. It is shown through simulation results that this scheme is more effective in both improving the control performance and reducing control force of the offshore platform than some existing ones, such as delay-free sliding mode control, nonlinear control, dynamic output feedback control, and delayed dynamic output feedback control. Furthermore, it is shown that the introduced time delay in this scheme can take values in different ranges while the corresponding control performance of the offshore platform is almost at the same level.

Abstract: This paper is concerned with the induced l2 dynamic output feedback controller (DOFC) design problem for discrete-time Markovian jump repeated scalar nonlinear systems. By employing both the switching-sequence dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique, a sufficient condition is first established, which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance. Then the desired full- or reduced-order DOFCs are designed by using projection approach. Cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem. Finally, a numerical example is presented to show the effectiveness of the proposed methods.

Abstract: This paper deals with the problem of controlling a hybrid energy storage system (HESS) for electric vehicles. The storage system consists of a fuel cell (FC), serving as the main power source, and a supercapacitor (SC), serving as an auxiliary power source. It also contains a power block for energy conversion consisting of a boost converter connected with the main source and a boost-buck converter connected with the auxiliary source. The converters share the same dc bus, which is connected to the traction motor through an inverter. These power converters must be controlled to meet the following requirements: 1) tight dc bus voltage regulation, 2) perfect tracking of the SC current to its reference, and 3) asymptotic stability of the closed-loop system. A nonlinear controller is developed, on the basis of the system nonlinear model, making use of Lyapunov stability design techniques. The latter accounts for the power converters' large-signal dynamics and for the FC nonlinear characteristics. It is demonstrated using both a formal analysis and simulations that the developed controller meets all desired objectives.

Abstract: This brief investigates the finite-time output feedback attitude control of a rigid spacecraft. First, a nonlinear observer is designed. Through geometric homogeneity and Lyapunov theories, it is shown that the proposed observer can achieve the semiglobal finite-time stability. Then, a finite-time output feedback controller is proposed based on the finite-time observer. Rigorous proof shows that the proposed control law ensures semiglobal stability and guarantees the attitude of a rigid spacecraft to track a time-varying reference attitude in finite time. Simulation results are presented to illustrate the performance of the proposed controller.

Abstract: This paper discusses the problem of adaptive neural network output feedback control for a class of stochastic nonlinear strict-feedback systems. The concerned systems have certain characteristics, such as unknown nonlinear uncertainties, unknown dead-zones, unmodeled dynamics and without the direct measurements of state variables. In this paper, the neural networks (NNs) are employed to approximate the unknown nonlinear uncertainties, and then by representing the dead-zone as a time-varying system with a bounded disturbance. An NN state observer is designed to estimate the unmeasured states. Based on both backstepping design technique and a stochastic small-gain theorem, a robust adaptive NN output feedback control scheme is developed. It is proved that all the variables involved in the closed-loop system are input-state-practically stable in probability, and also have robustness to the unmodeled dynamics. Meanwhile, the observer errors and the output of the system can be regulated to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach.

Abstract: This paper addresses stabilization issue of switched nonlinear systems where some modes are stable and others may be unstable. A new stabilizing switching law that determines the initial states and the switching instants for any given switching sequence is proposed. The developed technique relies on the tradeoff among the functions’ gains of continuous modes, and does not depend on the constant ratio condition required in “dwell-time scheme”.

Abstract: In this paper, an adaptive fuzzy output-feedback control is investigated for a class of pure-feedback uncertain nonlinear systems with unknown dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are used to identify the unknown nonlinear functions, and a state filter observer is designed to estimate the unmeasured states. Based on the information of the dead-zone slopes as well as treating the unknown inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. The stability of the resulting closed-loop system is proved and a simulation example is provided to show the effectiveness of the proposed control approach. The important feature of the proposed adaptive fuzzy controller is that it can solve the states immeasurable and the unknown dead-zone problems that exist in the previous publications and extends the existing results on strict-feedback control to the counterpart on pure-feedback control.

Abstract: This paper presents a new control topology to enable effective integration of voltage source converters (VSCs) in weak grids. The controller has two main parts. The first part is a linear power-damping and synchronizing controller which automatically synchronizes a VSC to a grid by providing damping and synchronizing power components, and enables effective full power injection even under very weak grid conditions. The controller adopts cascaded angle, frequency and power loops for frequency and angle regulation. The controller emulates the dynamic performance of synchronous machines, which eases grid integration and provides a virtual inertia control framework for VSCs to damp power and frequency oscillations. Although the linear controller offers stable and smooth operation in many cases, it cannot ensure system stability in weak grids, where sudden large disturbances rapidly drift system dynamics to the nonlinear region. To overcome this difficulty, a supplementary nonlinear controller is developed to assist the linear controller and enhance system performance under large-signal nonlinear disturbances, such as self-synchronization, disturbances in grid frequency and angle, high power injection in very weak grids and fault-ride-through conditions.

Abstract: This paper analyzes the dynamics of an offshore boom crane and proposes a high-performance nonlinear controller to drive the system states to track some constructed trajectories. Specifically, by employing Lagrange's method in an attached frame, a dynamic model is obtained for the offshore crane system consisting of the boom and a payload, with specific emphasis on the effect of the vessel's motion on the payload swing. Based on the model, a novel nonlinear control law is designed for the underactuated boom crane, which makes the system states track some planned trajectories successfully, even in the presence of persistent disturbance in harsh sea conditions. The stability of the designed closed-loop system is proven by Lyapunov techniques. Simulation and experimental results are included to demonstrate that the proposed control method significantly reduces the impact of the disturbance in harsh sea conditions.

Abstract: An approach to control tethered wings for airborne wind energy is proposed. A fixed length of the lines is considered, and the aim of the control system is to obtain figure-eight crosswind trajectories. The proposed technique is based on the notion of the wing's “velocity angle” and, in contrast with most existing approaches, it does not require a measurement of the wind speed or of the apparent wind at the wing's location. In addition, the proposed approach features few parameters, whose effects on the system's behavior are very intuitive, hence simplifying tuning procedures. A simplified model of the steering dynamics of the wing is derived from first-principle laws, compared with experimental data and used for the control design. The control algorithm is divided into a low-level loop for the velocity angle and a high-level guidance strategy to achieve the desired flight patterns. The robustness of the inner loop is verified analytically, and the overall control system is tested experimentally on a small-scale prototype, with varying wind conditions and using different wings.

Abstract: Good tracking performance is very important for trajectory tracking control of robotic systems. In this paper, a new model-free control law, called PD with sliding mode control law or PD-SMC in short, is proposed for trajectory tracking control of multi-degree-of-freedom linear translational robotic systems. The new control law takes the advantages of the simplicity and easy design of PD control and the robustness of SMC to model uncertainty and parameter fluctuation, and avoid the requirements for known knowledge of the system dynamics associated with SMC. The proposed control has the features of linear control provided by PD control and nonlinear control contributed by SMC. In the proposed PD-SMC, PD control is used to stabilize the controlled system, while SMC is used to compensate the disturbance and uncertainty and reduce tracking errors dramatically. The stability analysis is conducted for the proposed PD-SMC law, and some guidelines for the selection of control parameters for PD-SMC are provided. Simulation results prove the effectiveness and robustness of the proposed PD-SMC. It is also shown that PD-SMC can achieve very good tracking performances compared to PD control under the uncertainties and varying load conditions.