Terminal Weighting Matrix Research Articles

Model Predictive Control for Linear Parameter Varying Systems Using a New Parameter Dependent Terminal Weighting Matrix

In this paper, we propose a new robust model predictive control (MPC) technique for linear parameter varying (LPV) systems expressed as linear systems with feedback parameters. It is based on the minimization of the upper bound of finite horizon cost function using a new parameter dependent terminal weighting matrix. The proposed parameter dependent terminal weighting matrix for norm-bounded uncertain models provides a less conservative condition for terminal inequality. The optimization problem that satisfies the terminal inequality is solved by semi-definite programming involving linear matrix inequalities (LMIs). A numerical example is included to illustrate the effectiveness of the proposed method.

RECEDING HORIZON NEURAL H∞ CONTROL FOR A CLASS OF NONLINEAR UNKNOWN SYSTEMS

In this paper, we present new RHNHC (Receding Horizon Neural H∞ Control) for nonlinear unknown systems. First, we propose LMI (Linear Matrix Inequality) condition on the terminal weighting matrix for stabilizing RHNHC. Under this condition, noninceasing monotonicity of the saddle point value of the finite horizon dynamic game is shown to be guaranteed. Then, we propose RHNHC for nonlinear unknown systems which guarantees the infinite horizon H∞ norm bound and the internal stability of the closed-loop systems. Since RHNHC can deal with input and state constraints in optimization problem effectively, it does not cause an instability problem or give a poor performance in contrast to the existing neural H∞ control schemes.

Disturbance Attenuation for Constrained Discrete-Time Systems via Receding Horizon Controls

In this note, we propose new receding horizon H/sub /spl infin// control (RHHC) schemes for linear input-constrained discrete time-invariant systems with disturbances. The proposed control schemes are based on the dynamic game problem of a finite-horizon cost function with a fixed finite terminal weighting matrix and a one-horizon cost function with time-varying finite terminal weighting matrices, respectively. We show that the resulting RHHCs guarantee closed-loop stability in the absence of disturbances and H/sub /spl infin// norm bound for 2-norm bounded disturbances. We also show that the proposed schemes can easily be implemented via linear matrix inequality optimization. We illustrate the effectiveness of the proposed schemes through simulations.

Implementation of stabilizing receding horizon controls for time-varying systems

In this paper, a new stabilizing receding horizon control (RHC) scheme is proposed for linear discrete time-varying systems, which can be easily implemented by using linear matrix inequality (LMI) optimization. The control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix. The resulting stabilizing RHC scheme leads to time-varying finite terminal weighting matrices even for time-invariant systems, which is more general than in the case of using constant matrices. Based on the proposed scheme, another implementation method is also discussed for easy computation and numerical feasibility consideration of LMI optimization, although the second method does not guarantee the closed-loop stability theoretically. Through a simulation example, the effectiveness of the proposed schemes is illustrated.

Robust one-step receding horizon control of discrete-time Markovian jump uncertain systems

This paper proposes a receding horizon control scheme for a set of uncertain discrete-time linear systems with randomly jumping parameters described by a finite-state Markov process whose jumping transition probabilities are assumed to belong to some convex sets. The control scheme for the underlying systems is based on the minimization of the worst-case one-step finite horizon cost with a finite terminal weighting matrix at each time instant. This robust receding horizon control scheme has a more general structure than the existing robust receding horizon control for the underlying systems under the same design parameters. The proposed controller is obtained using semidefinite programming.

Receding horizon guidance laws for constrained missiles with autopilot lags

Abstract In this paper, a new stabilizing receding horizon control (RHC) scheme is proposed for linear continuous time-invariant systems with input and state constraints. The control scheme is based on the minimization of the finite horizon cost with a finite terminal weighting matrix subject to constraints. A new algorithm is suggested to implement the RHC scheme for a constrained receding horizon guidance law (CRHG). The proposed CRHG, which does not use information on the time-to-go, is obtained by using linear matrix inequality (LMI) optimization. Through simulation examples, the performance of the proposed CRHG is illustrated.

Output-Feedback Receding Horizon Controller Design for LTV Systems

This paper presents a dynamic output-feedback receding horizon controller (RHC) for LTV systems including periodic systems. The existing output-feedback RHC in the literature is composed of a state observer and a static controller associated with the observer states (similar to LQG control), where the fundamental assumption is that the state observer will supply the exact states as time goes up. When the system suffers from disturbances and uncertainties or is time-varying, however, the performance of those controllers may be much degraded and even the closed-loop stability may not be guaranteed. The proposed controller, which is not necessary to have the state-observer, overcomes such difficulties. Using matrix inequality conditions on the terminal weighting matrix, the closed-loop system stability is guaranteed.

A stabilizing static output feedback receding horizon control for linear discrete time-invariant systems

In this paper, a stabilizing static output feedback receding horizon control (RHC) is proposed for linear discrete time-invariant systems. Firstly, an inequality condition on the terminal weighting matrix is presented under which the closed-loop stability of static output feedback receding horizon controls is guaranteed. Then, it is shown that the stabilizing static output feedback receding horizon control problem can be represented as a nonlinear minimization problem based on linear matrix inequalities (LMl's). An algorithm for solving the nonlinear minimization problem is proposed. Finally, applications of the proposed controller are illustrated through numerical examples.

On receding horizon controls for time-delay systems

In this paper, a general receding horizon control is first proposed for time-delay systems. A linear matrix inequality(LMI) condition on the terminal weighting matrix is proposed for time-delay systems, under which nonincreasing monotonicity of the optimal cost is guaranteed. It is shown that the proposed terminal inequality condition with an additional observability condition guarantees closed-loop stability of receding horizon control(RHC). A RHC with input and state constraints is also proposed. Using the invariant ellipsoid constraints, a feasibility condition and a region of attraction are characterized for the proposed receding horizon control with input and state constraints.

Exponential stability of constrained receding horizon control with terminal ellipsoid constraints

In this paper, state- and output-feedback receding horizon controllers are proposed for linear discrete time systems with input and state constraints. The proposed receding horizon controllers are obtained from the finite horizon optimization problem with the finite terminal weighting matrix and the artificial invariant ellipsoid constraint, which is less restrictive than the conventional terminal equality constraint. Both hard constraints and mixed constraints are considered in the state-feedback case, and mixed constraints are considered in the output-feedback case. It is shown that all proposed state- and output-feedback receding horizon controllers guarantee the exponential stability of closed-loop systems for all feasible initial sets using the Lyapunov approach.

On Stability of Constrained Receding Horizon Control with Finite Terminal Weighting Matrix

In this paper, a new stabilizing receding horizon control, based on a finite input and state horizon cost with a finite terminal weighting matrix, is proposed for time-varying discrete linear systems with constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed-loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints. We show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality (LMI). In the case of constrained time-invariant systems, an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control.

Implementable Receding Horizon Control for Constrained Systems

In this paper, new state feedback and output feedback receding horizon controllers, based on a finite input and state horizon cost with a finite terminal weighting matrix, are proposed for discrete linear systems with input and state constraints. We propose matrix inequality conditions on the terminal weighting matrix under which closed loop exponential stability is guaranteed for both cases of state feedback and output feedback. We show that such a terminal weighting matrix can be obtained by solving an LMI (Linear Matrix Inequality). An artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints. Using the invariant ellipsoid constraints, a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control. A couple of illustrative examples are included.

Receding horizon H tracking control for time-varying discrete linear systems

In this paper, a new receding horizon tracking control law based on the H control concept, is proposed for time-varying discrete linear systems. The proposed controller is constructed using a dynamic game approach minimizing a worst case finite horizon performance index with the finite terminal weighting matrix. The conditions on the terminal weighting matrix are proposed under which the proposed control law guarantees closed loop stability and, simultaneously, the infinite horizon H norm bound. It is shown that the proposed stability condition on the terminal weighting matrices can be converted to a Linear Matrix Inequality (LMI). In order to prove closed-loop stability, the monotonicity property of the cost is utilized instead of the monotonicity property of the Riccati equation. It is also shown that the proposed stability condition on both terminal weighting matrices and the cost horizon size are more general than the conventional results. Some examples are included to illustrate the proposed results.