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 linea...
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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.< >
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 syste...
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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.
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 termina...
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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.
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...
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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 backstepping tools and demonstrate how they can be used in systematic design procedures.< >
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...
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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 for robust global stabilizability via continuous static or dynamic measurement feedback.< >
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 disconti...
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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.
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 ...
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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.
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 h...
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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
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 fo...
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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.
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.
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