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Nonlinear control system design via dynamic order reduction

Nonlinear control system design via dynamic order reduction

引用

IEEE Conference on Decision and control

作者： R. Ghanadan Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

In this paper we present a design scheme for output tracking of nonlinear systems that are subject to regular perturbations. We show that applications of singular perturbation theory to the input-output feedback linearization technique provides a systematic method to identify the slow "dominant" states and fast "negligible" states. Similar to the backstepping design technique, a suitable state variable is converted into a "control like" variable which in the steady state is forced to approach the desired tracking control law for the reduced order system. We show that this design achieves stable approximate tracking of reasonable reference trajectories for nonlinear systems that are "dominantly" minimum phase. The order of approximation can be arbitrarily improved by addition of correction terms in the control law. The main advantage of this approach is that the design is often performed for a much simpler model which is linear in the new control variable and describes the dominant part of the original system by ignoring some of the fast states that are forced to have little effect on the steady state performance.< >

关键词： Nonlinear control systems Nonlinear dynamical systems Nonlinear systems Steady-state Force control State feedback Linearization techniques Backstepping control systems Reduced order systems

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A "Throw-and-Catch" Hybrid control Strategy for Robust Global Stabilization of Nonlinear Systems

A "Throw-and-Catch" Hybrid Control Strategy for Robust Globa...

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American control Conference (ACC)

作者： Ricardo G. Sanfelice Andrew R. Teel Electrical and Computer Engineering Department Center for Control Engineering and Computation University of California Santa Barbara CA USA

We present a control strategy that combines local state feedback laws and open-loop schedules to robustly globally asymptotically stabilize a compact subset (typically a point) of the state space for a nonlinear system. The control algorithm is illustrated on the problem of global stabilization of the upright position of the pendubot and implemented in a hybrid controller containing logic variables and logic rules with hysteresis. We also present the design procedure of the hybrid controller for general nonlinear systems. Recent results in the literature on robustness of asymptotic stability in hybrid systems are used in establishing that the closed-loop system is robust to measurement noise and other external disturbances.

关键词： Nonlinear control systems control systems Robust control Nonlinear systems Open loop systems Logic Noise robustness Robust stability State feedback State-space methods

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Nominally robust model predictive control with state constraints

Nominally robust model predictive control with state constra...

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IEEE Conference on Decision and control

作者： G. Grimm M.J. Messina S.E. Tuna A.R. Teel Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

We present robust stabilization results for constrained, discrete-time, nonlinear systems using a finite-horizon model predictive control (MPC) algorithm that does not require any particular properties for the terminal cost. We introduce a property that characterizes the robustness properties of the MPC optimization problem. Assuming the system has this property (for which we give sufficient conditions), we make two further key assumptions. These are that the value function is bounded by a K/sub /spl infin// function of a state measure (related to the distance of the state to some target set) and that this measure is detectable from the stage cost used in the MPC algorithm. We show that these assumptions lead to stability that is robust to sufficiently small disturbances and measurement noise. While in general the results are semiglobal practical, when the detectability and upper bound assumptions are satisfied with linear K/sub /spl infin// functions, the stability and robustness is global with respect to the feasible set. We discuss algorithms employing terminal equality or inequality constraints. We provide two examples, one involving a terminal equality constraint and the other involving a nonrobustness-inducing state constraint.

关键词： Robust control Predictive models Predictive control Robust stability Noise robustness Nonlinear systems Prediction algorithms Sufficient conditions Cost function Noise measurement

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Tools and procedures for robust control of nonlinear systems

Tools and procedures for robust control of nonlinear systems

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IEEE Conference on Decision and control

作者： R.A. Freeman P.V. Kokotovic Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

We review some of the existing results on the Lyapunov design of robustly stabilizing feedback laws for uncertain nonlinear systems. Using the concept of a robust control Lyapunov function, we present robust backstepp... 详细信息

关键词： Robust control Nonlinear systems Lyapunov method Feedback control systems Force control Asymptotic stability Nonlinear control systems control engineering control engineering computing

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Robust control Lyapunov functions: the measurement feedback case

Robust control Lyapunov functions: the measurement feedback ...

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IEEE Conference on Decision and control

作者： R.A. Freeman P.V. Kokotovic Center for Control Engineering and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA USA

We extend the concept of a robust control Lyapunov function (RCLF) for nonlinear systems to the case of measurement feedback. We explore conditions under which the existence of an RCLF is sufficient and/or necessary f... 详细信息

关键词： Robust control Computer aided software engineering State feedback Lyapunov method Robustness control systems Uncertain systems control engineering control engineering computing Nonlinear systems

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Global asymptotic stabilization of the inverted equilibrium manifold of the 3-D pendulum by hybrid feedback

Global asymptotic stabilization of the inverted equilibrium ...

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IEEE Conference on Decision and control

作者： Christopher G. Mayhew Andrew R. Teel Center of Control Engineering and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

Topological obstructions preclude the existence of a continuous state-feedback control law that globally asymptotically stabilizes the inverted equilibrium manifold of the 3D pendulum. Furthermore, memoryless discontinuous feedbacks are either unbounded or not robust to arbitrarily small measurement noise. In this paper, we propose a hybrid feedback that coordinates a “synergistic” family of potential functions and their gradient-based feedbacks to ensure global asymptotic stability of the inverted equilibrium manifold of the 3D pendulum. The hybrid scheme is robust to small perturbations including measurement noise, eliminates performance limitations of smooth state feedback, and obviates the need for large torques created by some non-smooth state-feedback control laws. We provide a brief simulation study to illustrate the efficacy of the method and compare it with a smooth feedback.

关键词： Three dimensional displays Manifolds Noise Robustness Noise measurement Gravity Switches

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Convexity in zero-sum differential games

Convexity in zero-sum differential games

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IEEE Conference on Decision and control

作者： R. Goebel Center for Control Engineering & Computation Department of Electrical & Computer Engineering University of California Santa Barbara CA USA

A new approach to two-player zero-sum differential games with convex-concave cost function is presented. It employs the tools of convex and variational analysis. A necessary and sufficient condition on controls to be an open-loop saddle point of the game is given. Explicit formulas for saddle controls are derived in terms of the subdifferential of the function conjugate to the cost. Existence of saddle controls is concluded under very general assumptions, not requiring the compactness of control sets. A Hamiltonian inclusion, new to the field of differential games, is shown to describe equilibrium trajectories of the game.

关键词： Cost function Open loop systems Sufficient conditions Differential equations control engineering control engineering computing Integral equations

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On the Continuity of Asymptotically Stable Compact Sets for Simulations of Hybrid Systems

On the Continuity of Asymptotically Stable Compact Sets for ...

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IEEE Conference on Decision and control

作者： Ricardo G. Sanfelice Andrew R. Teel Center for Control Engineering and Computation Electrical and Computer Engineering Department University of California Santa Barbara CA USA

ISBN: (纸本)1424401704;9781424401703

We propose a hybrid model for simulations of hybrid systems and we establish conditions on its data so that the asymptotically stable sets observed in simulations are continuous. The most important components of the hybrid model for simulations are a discrete integration scheme for the computation of the flows and an approximated jump mapping for the computation of the jumps. Our main result is built on the facts that, on compact hybrid time domains, every simulation to a hybrid system is arbitrarily close (in the graphical sense) to some solution to the actual hybrid system, and that asymptotically stable compact sets of hybrid systems are semiglobally practically asymptotically stable compact sets for the hybrid model for simulations. We present these results and illustrate them in simulations of the bouncing ball system

关键词： computational modeling Differential equations State-space methods Numerical simulation Analytical models Military computing USA Councils Standards development control systems Packaging

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Complex hybrid systems: Stability analysis for omega limit sets

Complex hybrid systems: Stability analysis for omega limit s...

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26th Chinese control Conference, CCC 2007

作者： Chaohong, Cai Rafal, Goebel Sanfelice, Ricardo G. Teel, Andrew R. Center for Control Dynamical Systems and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA 93106-9560 United States 3518 NE 42 St. Seattle WA 98105 United States

ISBN: (纸本)7900719229

This paper focuses on the asymptotic stability properties of omega limit sets for complex hybrid dynamical systems, which are commonly found in systems and engineering. It spells out specific stability results that follow when a hybrid dynamical system has certain structure, e.g., when it admits a decomposition resembling a cascade of hybrid dynamical systems.

关键词： Dynamical systems

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Hybrid dynamical systems: Robust stability and control

Hybrid dynamical systems: Robust stability and control

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26th Chinese control Conference, CCC 2007

作者： Cai, Chaohong Rafal, Goebel Sanfelice, Ricardo G. Teel, Andrew R. Center for Control Dynamical Systems and Computation Department of Electrical and Computer Engineering University of California Santa Barbara CA 93106-9560 United States 3518 NE 42 St. Seattle WA 98105 United States

Modeling issues for hybrid dynamical systems are discussed and fundamental stability analysis tools are summarized. These tools are useful for the development of hybrid control algorithms.

ISBN: (纸本)7900719229

Modeling issues for hybrid dynamical systems are discussed and fundamental stability analysis tools are summarized. These tools are useful for the development of hybrid control algorithms.

关键词： control systems

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