This paper develops a model-free H-infinity control design algorithm for unknown linear discrete-time systems by using Q-learning, which is a reinforcement learning method based on an actor-critic structure. In model-...
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This paper develops a model-free H-infinity control design algorithm for unknown linear discrete-time systems by using Q-learning, which is a reinforcement learning method based on an actor-critic structure. In model-free design, there is no known dynamical model of the system. Thus, one has no information on the system matrices, but can access the state variables and input variables. The paper derives an iterative solution algorithm for H-infinity control design that is based on policy iteration. The algorithm is expressed in the form of linear matrix inequalities (LMI) that do not involve the system matrices, but only require data measured from the system state and input. It is shown that, for sufficiently rich enough disturbance, this algorithm converges to the standard H-infinity control solution obtained using the exact system model. Two numerical examples are given to show the effectiveness in obtaining the H-infinity control without any using knowledge of the system dynamics matrices, and the examples show that the results converge to the ones obtained with the exact system dynamics matrices. (C) 2010 Elsevier Ltd. All rights reserved.
Abstract This paper presents a data-driven algorithm for tracking control of a lineardiscrete-time plant. No traditional mathematical model of the plant such as transfer function or state equation is employed. Instea...
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Abstract This paper presents a data-driven algorithm for tracking control of a lineardiscrete-time plant. No traditional mathematical model of the plant such as transfer function or state equation is employed. Instead, the plant dynamics is represented by an array whose elements are plant input-output data. Sensitivity of the array to input and output noise is introduced. Then, it is shown that, for an arbitrary reference signal, the tracking control input which minimizes the sensitivity can readily be computed by solving a linear matrix inequality which is composed of the array.
In this paper we study the H(infinity) tracking problems with preview for a class of linear continuous-timesystems with impulsive effects. The systems include linear continuous-timesystems, lineardiscrete-time syst...
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ISBN:
(纸本)9781424453634
In this paper we study the H(infinity) tracking problems with preview for a class of linear continuous-timesystems with impulsive effects. The systems include linear continuous-timesystems, linear discrete-time systems and linearsystems with the input realized through a zero-order hold. The necessary and sufficient conditions for the solvability of the H(infinity) tracking problem are given by Riccati differential equations with impulsive effects and terminal conditions. Correspondingly feedforward compensator introducing future information is given by linear differential equation with impulsive parts and terminal conditions. In this paper we focus on the derivation method of noncausal compensator dynamics from the point of view of dynamics constraint. We derive the pair of noncausal compensator dynamics and impulsive Riccati equations by calculating the first variation of the performance index under the dynamics constraint.
This note discusses a relationship between the Hankel singular values and reflected zeros of linearsystems. Our main result proves that the Henkel singular values or a linear continuous-timesystem increase (decrease...
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This note discusses a relationship between the Hankel singular values and reflected zeros of linearsystems. Our main result proves that the Henkel singular values or a linear continuous-timesystem increase (decrease) pointwise when one or more zeros of the transfer function are reflected with respect to the Imaginary axis, that Is, move from the left-(right)half to the right-(left-)hair of the complex plane. We also derive a similar result for linear discrete-time systems.
Directional interpolation plays an important role in robust control, system realization and model reduction. Several solutions to various directional interpolation problems have been proposed. In this paper, we consid...
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Directional interpolation plays an important role in robust control, system realization and model reduction. Several solutions to various directional interpolation problems have been proposed. In this paper, we consider the directional interpolation problem in a general setting and present a statespace based new approach to solving the problem. The solution is simple, and its exposition is as self-contained as possible. We describe all the (strictly) bounded real rational matrix functions that satisfy the directional interpolation requirements by means of linear fractional transformation. Moreover, we give a necessary and sufficient condition for the interpolating function to be unique and show that the unique interpolating function is an inner (a co-inner). The main procedures used to generate the interpolating function consist of standard matrix operations consisting of easy numerical computations, so the present solution is significant from the numerical viewpoint as well as the analytical viewpoint.
A VSC (Variable Structure Control) scheme based on SVM (Support Vector Machine) and SSS (Shift Switching Surface) is developed. Based on SSS and VSC reaching law, a control scheme for tracking control system is propos...
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ISBN:
(纸本)9787811240559
A VSC (Variable Structure Control) scheme based on SVM (Support Vector Machine) and SSS (Shift Switching Surface) is developed. Based on SSS and VSC reaching law, a control scheme for tracking control system is proposed, and an additional control is introduced to reduce effect of disturbance. Then SVM is introduced to realize VSC for black-box system. The scheme is simple, and the robustness is proven in simulation.
We study robustness of -stability of linear difference equations under multiperturbation and affine perturbation of coefficient matrices via the concept of -stability radius. Some explicit formulae are derived for the...
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We study robustness of -stability of linear difference equations under multiperturbation and affine perturbation of coefficient matrices via the concept of -stability radius. Some explicit formulae are derived for these -stability radii. The obtained results include the corresponding ones established earlier in Hinrichsen and Son and Ngoc and Son as particular cases.
We study robustness of 𝒟-stability of linear difference equations under multiperturbation and affine perturbation of coefficient matrices via the concept of 𝒟-stability radius. Some explicit formulae a...
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We study robustness of 𝒟-stability of linear difference equations under multiperturbation and affine perturbation of coefficient matrices via the concept of 𝒟-stability radius. Some explicit formulae are derived for these 𝒟-stability radii. The obtained results include the corresponding ones established earlier in Hinrichsen and Son and Ngoc and Son as particular cases.
On the basis of the relationship of the mth power of a polynomial and its modular form (polynomial whose coefficients are the moduli of the coefficients of that polynomial), we derive a necessary and sufficient condit...
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On the basis of the relationship of the mth power of a polynomial and its modular form (polynomial whose coefficients are the moduli of the coefficients of that polynomial), we derive a necessary and sufficient condition for the modulus of the mth power of a polynomial for contacting its modular form on the boundary of a disc. Combined with the result about distribution of zeros of analytic function, some new sufficient conditions are derived which give bounds of the absolute values of the roots of a quasi-critical polynomial. These results extend certain earlier similar tests for linear discrete-time systems. Finally, four examples are given to demonstrate the results, Example 2.1 gives a state feedback application, Examples 2.2 and 2.4 deal with r-stability, and Example 2.3 display that our theorems give better results when m increases but at the cost of increasing complexity.
Ellipsoidal invariant sets of linear discrete-time systems are treated to approximate the reachable sets for bounded inputs. All the ellipsoids are parameterized by a bilinear matrix inequality. The criteria for the e...
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Ellipsoidal invariant sets of linear discrete-time systems are treated to approximate the reachable sets for bounded inputs. All the ellipsoids are parameterized by a bilinear matrix inequality. The criteria for the ellipsoids are defined to represent the degrees of approximations. The optimal ellipsoids can be obtained by the convex optimizations with one scalar variable. The efficiency of the proposed method is demonstrated in a numerical example in comparison with a method of previous research.
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