This article studies the finite-time output regulation problem for linear time-invariant continuous-time systems. By using the solution to a parametric Lyapunov equation (PLE) and regulator equations, three bounded linear time-varying (LTV) state controllers composed of the LTV feedback gain and the LTV feedforward gain are designed, such that (prescribed) finite-time output regulation is solved. As a further result, a linear LTV observer-based controller is also designed. The most significant advantages of this article are that the system under consideration is more general and the output regulation problem is achieved within a user-chosen regulation time. Finally, the developed LTV state controllers are utilized to the design of the satellite formation flying control system and simulation results verify the effectiveness of the proposed approaches.
In this paper, a new value iteration (VI) based method is proposed to solve the H ∞ control problem of continuous-time linear systems. The problem is transformed into solving a nonlinear differential equation, and the local stability of its solution is proved. Then a VI based iteration scheme for getting the approximation of the H ∞ optimal controller is proposed. Compared with the existing results, the proposed scheme does not need any special initial matrix or extra condition to solve the problem and provides a relatively small disturbance attenuation bound. The related result is also applied to the quadratic guaranteed cost control of linear time-delay systems. Simulation examples verify the effectiveness of the proposed schemes.
K E Y W O R D Sadaptive dynamic programming, linear H ∞ control, model free control, time-delay systems, zero-sum differential games
INTRODUCTIONOver the past few decades, the analysis and control of systems with disturbance and complex dynamics have received considerable attention in the control community. 1,2 As one of the most popular methods, H ∞ control, which studies the problem of the worst-case controller design, [3][4][5] was established and flourished. One way for solving the H ∞ control problem is to treat it as an infinite-horizon zero-sum game problem where the input of the system tries to minimize the infinite quadratic cost function and the disturbance tries to maximize it. Especially, by treating the delayed state as the disturbance, the H ∞ optimal control method can also solve the quadratic cost guaranteed control of systems with state delays. 6 The synthesis of the H ∞ controller needs to solve the Hamilton-Jacobi-Isaacs equations for nonlinear systems 7 and the game algebraic Riccati equation (GARE) for linear systems. 8 For linear systems, solving the GARE can be divided into two categories: the direct method 9,10 and the iterative method. 11,12 Both methods mentioned above need the exact system information of the original systems, which is however hard to be satisfied since in practice the system parameters usually contain uncertainties and thus are unknown. Therefore, how to solve the H ∞ optimal control problems without using the exact system parameters has attracted much attention in the literature.One way for dealing with the system uncertainties is to use the adaptive dynamic programming (ADP) method. In recent years, ADP has attracted more and more attention from both control theorists and engineers. It overcomes the curse of dimensionality 13,14 and acts as a promising methodology for solving the optimal control problem. [15][16][17][18] By ADP,
This article studies semiglobal stabilization of input constrained linear systems based on the static and dynamic event-triggered control (ETC) and self-triggered control (STC). First, a static ETC based on the parametric Lyapunov equation (PLE) is designed. Then the corresponding dynamic ETC is also proposed. The main advantage of the proposed static and dynamic ETC algorithms is that the minimum interexecution time (MIET) as a decreasing function of the parameter in the PLE is given, which allows us to find easily a trade-off between the interexecution times (IETs) and the control performance. The fact that the MIET of the dynamic ETC is never less than that of the static ETC is also guaranteed. Next, in order to avoid continuous monitoring of the states, both static and dynamic STC are designed. The influence of the parameters on IETs of the static and dynamic STC is analyzed in detail. The nonoccurrence of the Zeno phenomenon is proved in all the control algorithms. Finally, the proposed algorithms are applied to the design of spacecraft rendezvous. Numerical simulations on the original nonlinear model of the spacecraft rendezvous control system show the control system effectiveness of the algorithms.
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