Abstract: A sequential numerical algorithm is described which obtains gains minimizing a broad class of performance indexes, including the standard LQ case. The primary contribution is a proof that the algorithm converges to a local minimum under nonrestrictive assumptions. Numerical examples illustrate the theory. The second example demonstrates an important LQ design technique which permits the designer to prespecify the feedback structure, subject to the requirement of output feedback stabilizability.

Abstract: The motion control of robotic manipulators is investigated using a recently developed approach to linear multivariable control known as the stable factorization approach. Given a nominal model of the manipulator dynamics, the control scheme consists of an approximate feedback linearizing control followed by a linear compensator design based on the stable factorization approach. Using a multiloop version of the small gain theorem, robust trajectory tracking is shown under the assumption that the deviation of the model from the true system satisfies certain norm inequalities. In turn, these norm inequalities lead to quantifiable bounds on the tracking error.

Abstract: We indicate how techniques from fixed point and degree theory may be combined with the linear theory of control and observation, to create controllability and observability results for a certain class of non-linear systems.

Abstract: High-gain state and output feedback are investigated for non-linear control systems with a single additive input by using singular perturbation techniques. Classical approximation results (Tihonov-like theorems) in singular perturbation theory are extended to non-linear control systems by defining a composite additive control strategy, a control-dependent fast equilibrium manifold and non-linear change of coordinates. Those tools and an appropriate change of coordinates show that high-gain state feedback and variable structure control systems can be equivalently used for approximate non-linearity compensation in feedback-linearizable systems. Next the effect of high-gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility. For strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input-output feedback-linear...

Abstract: Given an uncertain dynamical system with a linear nominal part, matched uncertainties, and a measured output, a sufficient condition is given for the existence of an output feedback stabilizing controller. For the general multiinput multioutput case, checking the sufficient condition involves the selection of a matrix F . For the special class of single input single output systems, F is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real, then an output feedback stabilizing controller does indeed exist.

Abstract: This brief paper demonstrates the concept of linear feedback equivalence for an exothermic eontinu-ous stirred tank reactor with first order kinetics. Feedback control is achieved by finding a transformation for the nonlinear system which carries this system into a linear controllable system in Brunovsky canonical form. A linear state feedback controller is then designed which achieves control over a broad range of operating conditions. This example demonstrates how recent developments in nonlinear control theory can be applied to chemical systems without relying on the usual methods of local linearization.

Abstract: We propose a new model-following control scheme for a class of nonlinear plants. The feedback control signal is a continuous function of all its arguments. It is shown that this scheme guarantees that tracking error remains bounded and tends to a neighborhood of the origin with a rate not inferior to an exponential one; furthermore, it allows the designer to arbitrarily prescribe the rate of convergence and the size of the set of ultimate boundedness.

Abstract: In this paper we continue our development of the analogues for nonlinear systems of those frequency domain notions so important in classical control. One of our long-term goals, about which we can now say quite a bit in a reasonably broad framework (see 4), is to develop a design philosophy for the construction of (globally) stabilizing compensators for nonlinear systems, based on seemingly familiar notions such as the (strong) relative degree of a nonlinear system or knowledge that the system is "minimum phase." Aside from the development of a basic, "frequency domain package" for nonlinear systems, this paper contains applications to system invertibility, (global) stabilization by dynamic compensation, and global linearization by state feedback for nonlinear systems with relative degree or minimum phase properties.

Abstract: An adaptive model following control law for nonlinear robotic systems with rotational joints is presented. The derivation of the controller does not require any knowledge of nonlinear system matrics and the uncertainty in the system. In the closed-loop system the joint angles asymptotically converge to the reference trajectories.

Abstract: Given a dynamical system whose description includes time-varying uncertain parameters, it is often desirable to design an output feedback controller leading to uniform stability of a given equilibrium point. When designing such a controller, one may consider static (i.e., memoryless) or dynamic compensation. In this paper, we show that solvability of various output feedback design problems is equivalent to existence of a solution to a certain Constrained Lyapunov Problem (CLP). The CLP can be stated in purely algebraic terms. Once the CLP is described, we provide necessary and sufficient conditions for its solution to exist. Subsequently, we consider application of the CLP to a number of robust stabilization problems involving static output feedback and observer-based feedback.

Abstract: In this paper we investigate the motion control of robotic manipulators using the recently developed stable factorization approach to tracking and disturbance rejection. Given a nominal model of the manipulator dynamics, the control scheme consists of an approximate feedback linearizing control followed by a linear compensator design based on the stable factorization approach to achieve optimal tracking and disturbance rejection. Using a multiloop version of the small gain theorem [17], the applicability of the linear design techniques and the stability of the closed loop system are rigorously demonstrated.

Abstract: In this paper we deal with the problem of finding a feedback under which the input-output behavior of a nonlinear system becomes exactly the same as that of a specified linear model. The solvability of this problem is shown to depend on a formal infinite zero structure associated with the system.

Abstract: Invariant distributions are defined for discrete-time nonlinear control systems, and necessary and sufficient conditions are given for their controlled invariance. This extends to discrete-time systems the basic tool which has been so important in solving the various synthesis problems for continuous-time systems. To indicate their utility in the discrete-time setting, they are used to locally solve the disturbance decoupling problem.

Abstract: This note is concerned with the problem of stabilizing an uncertain linear system via state feedback control. An uncertain system which admits a stabilizing state feedback control and some associated quadratic Lyapunov function is said to be quadratically stabilizable. In a number of recent papers, conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control. These papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result. This note presents an example which shows that this implication is not true for more general uncertain linear systems. To this end, we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control.

Abstract: A definition of zeros at infinity for affine nonlinear control systems is proposed. The definition is local, which means that we exclude certain singularities. We argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling. In particular, we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity.

Abstract: In this paper a controller theory is introduced for multivariable 2-D systems together with stabilization algorithms based on state and output feedback techniques.

Abstract: A definition of zeros at infinity for affine nonlinear control systems is proposed. The definition is local, which means that we exclude certain singularities. We argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling. In particular, we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity.

Abstract: We study tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator. Roughly speaking, we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

Abstract: We consider a rational nonlinear equation which is involved in the general synthesis (design) problem of linear multivariable systems. The complete solution of this equation, subject to causality, stability, and minimality constraints, is provided. Formal power series and, in particular, the theory of partial realizations, prove of central importance for the design problem.

Abstract: The generalized singular linear quadratic (GSLQ) control technique is developed to design an optimal time-varying trajectory tracking system. The feedforward command in this system is generally computed by integrating a reduced-order system backward in time with the Future desired trajectory and the estimated disturbance or nonlinearity as the input. The output feedback control law is designed using the GSLQ contra1 techniqqe. The feedback gain matrix is synthesized to ' minimize tracking errors with pole placement capability to satisfy the control activity requirements. The resulting tracking system is capable of determining the current optimal control strategy based on the future desired trajectory. The modeling error terms such as the uncertainty, nonlinearity, and the anticipated forcing function are included in the GSLQ control problem formulation, enabling the resulting control law to adapt to these modeling changes as long as they can be approximately estimated on-line. An application of the GSLQ technique to a bank-to-turn (BlT.) missile coordinated autopilot system design is presented. The time varying tracking autopilot is f rmulated as an optimal linear tracking system pro lem consisting of an adaptive feedforward control er and a robust output feedback controller wi if robust output feedback gains, both designed b the GSLQ control technique. The closed loop system of the resulting control law is stable for a wide range of flight conditions with little changes in the location of the closed loop eigenvalues. The control loop frequency response of six flight conditions during the terminal phase are presented to show the robustness of an output feedback controller design using the GSLQ technique. Simulations of the time responses of the tracking system with sinusoidal wave disturbances and pitch, roll, and yaw nonlinear couplings are also presented to show the GSLQ control technique for tracking autopilot with adaptive feedforward control.

Abstract: Sufficient conditions for the local and global controllability of general nonlinear systems, by means of controls belonging to a fixed finite-dimensional subspace of the space of all admissible controls, are established with the aid of topological methods, such as homotopy invariance principles. Some applications to certain classes of nonlinear control processes are given, and various known results on the controllability of perturbed linear systems are also derived as particular cases.

Abstract: The problem of constant gain output feedback regulator design for linear systems with ill-conditioned dynamics is considered in the context of singular perturbation theory. A design approach is developed in which gains can be separately calculated to stabilize reduced-order slow and fast subsystem models. By employing the notion of combined control and observation spillover suppression, conditions are derived assuring that these gains will stabilize the full-order system, assuming sufficient frequency separation between the slow and fast subsystems. An LQ design procedure is described in which the spillover suppression conditions are satisfied by adjoining penalty functions to the subsystem performance indices. The theory is demonstrated in a controller design for a flexible space structure.

Abstract: In this paper we consider the control problem for a class of coupled, second-order singularly perturbed nonlinear dynamical systems. The problem has important application to flexible mechanical systems including robot manipulators with flexible joinra, where the singular perturbation parameter ? is the inverse of the joint stiffness. For this class of systems it is known that the reduced order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear state feedback, but that the full order flexible system is not, in general, linearizable. We utilize the concept of integral manifold to represent the dynamics of the slow subsystem, which reduces to the rigid model as the perturbation parameter tends to zero. We show that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around ? = 0 we show how to approximate the feedback linearizing control to any order in ?. The result is a nonlinear feedback control scheme to "stiffen" the nonlinear flexible system. That is, the behavior of the closed loop flexible system is nearly that of the controlled rigid system.

Abstract: Strong similarities between control theory and the theory on the solution of operator equations have been observed and basic results in control theory have been derived from operator theory arguments. The purpose of this work is to use the underlying duality in order to develop analysis and synthesis techniques for nonlinear systems. As an example, controllers induced by the Newton method are introduced and the corresponding stability characteristics are studied. The concepts are demonstrated by applications to linear and nonlinear systems.

Abstract: An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.

Abstract: It is shown that nonlinear feedback with diffeomorphic state transformation is applicable to dynamic control of PUMA 560 robot arm. This new dynamic control method externally (or exactly) linearizes the whole system and provides simultaneous output decoupling. To render the control robust, the nonlinear feedback is augmented with optimal error correcting controller which operates on the error in the task space. A key feature of this dynamic control method is that the nonlinear gains in the controller do not need readjustment from task to task. In that sense this controller is "intelligent" since it directly responds to changing task commands. A complete dynamic model in state equation form and with the necessary geometric and inertial parameters is also presented for PUMA 560 restricted to motions at the first three joints. This model is necessary to specify the nonlinear feedback and diffeomorphic transformation.