Yuzo Ohta

On-line reference management for discrete-time servo systems under state and control constraints

This paper proposes a method of discrete time servo systems design and on-line management of reference signals so as not to violate state and control constraints. The stabilizing and reference shaping controllers are designed off-line by solving LMI optimization problems that takes into account both LQR characterization and state and control constraints. Our managed reference is a piecewise constant signal which is determined online. The better performance of the proposed approach for cases that the initial state is disturbed is demonstrated through an example.

On the construction of piecewise linear Lyapunov functions

The issue of constructing piecewise linear Lyapunov functions (PLLFs) for the stability analysis of polytopic uncertain linear systems is considered. PLLF candidates are parametrized by hyperplanes which intersect the given region, and stability conditions are formulated as linear programming (LP) problems in terms of the parameters inserted by the hyperplanes. If the optimal value of the LP problem is negative, then the PLLF is constructed by using the optimal solution. When the optimal value of the LP problem is non-negative, the candidate PLLF is modified by adding new dividing hyperplanes to increase the freedom, and a new LP problem is formulated corresponding to the new PLLF candidate. The main result of this paper is to propose a method generating additional dividing hyperplanes which strictly decrease the optimal values of the LP problems which appear in constructing PLLFs. An example is used to illustrate the obtained results.

A Dual Mode Reference Governor for Discrete Time Systems with State and Control Constraints

In this paper, a dual mode reference governor for discrete-time systems with constraints in input and state is proposed. The reference governor manages reference command at the first stage, and then manages switching of controllers so that it achieves better performance of servo systems. A new LMI formulation to design controllers which gives rather large maximal admissible sets is proposed.

On Approximation of Maximal Admissible Sets for Nonlinear Continuous-Time Systems with Constraints

The concept of the maximal admissible set (MAS) is very important in several issues in control theory, such as constrained control and so on. For linear uncertain discrete time systems, a method to compute the MAS was proposed. For linear time invariant systems without uncertainty, a theoretical result on inner and outer approximations of the MAS was derived. On the other hand, for uncertain and/or nonlinear continuous time systems, only a few restrictive results were reported. This paper treats uncertain and/or nonlinear continuous time systems with constraints and derive some theoretical results about inner and outer approximations of the MAS for such a kind of systems.

Stability analysis of nonlinear systems via piecewise linear Lyapunov functions

This paper addresses the issue of constructing piecewise linear Lyapunov functions (PWLLF) for nonlinear systems satisfying the generalized sector condition, which is a generalization of the polytopic uncertainty. The main result of this paper is to propose a fast method to solving linear programming problems (LPs) which appear repeatedly in constructing PWLLF. The method uses a special structure of LPs which appear in constructing PWLLF.

A generalization of piecewise linear Lyapunov functions

The purpose of this paper is to propose a generalization of piecewise linear Lyapunov functions (PLLFs). In original PLLF candidates, functions are parameterized by hyperplanes, which intersect the stability region and stability conditions are formulated as linear programming problems (LPs) in terms of the parameters inserted by the hyperplanes. The piecewise linear hyperplanes (PLHPs) were introduced to reduce the size of LPs and produce a new class of PLLF candidates; however, applicable systems of this idea were restricted in a certain class of systems. In this paper, this restriction is removed and new PLLF candidates are characterized as the sum of piecewise linear functionals corresponding to PLHPs.

Stability analysis of discontinuous nonlinear systems via piecewise linear Lyapunov functions

The purpose of this paper is to present a stability analysis of discontinuous nonlinear systems using piecewise linear Lyapunov functions (PWLLF). The functions are parametrized by hyperplanes, which intersect the stability region, and stability conditions are formulated as linear programming problems (LP) in terms of the parameters inserted by the hyperplanes. An interesting feature of the analysis is that it can include the uncertainty caused by time delays which are inherent in switching devices controlling the system. A few examples are used to illustrate the obtained results.

Sliding Mode Control under State and Control Constraints

In this paper, we propose a method of continuous-time sliding mode control(SMC) system design so as not to violate state and control constraints. To circumvent chattering problem, we use continuous control law. And, we employ the inner approximation of maximal admissible set for a nonlinear continuous-time system to guarantee the satisfaction of constraints. This approach has the advantages that it is robust over initial state error and that save the on-line computing time required to inclusion check of maximal admissible sets. Moreover, we propose a control strategy of switching sliding hyperplanes to achieve better performance.

Robust stabilization and enlargement of attractive region of control systems using piecewise linear Lyapunov functions

The purpose of this paper is to present a method to design control gain matrices by using piecewise linear Lyapunov functions so that closed systems are robust stable and attractive regions are as large as possible in given polytopic regions. The design problems for these specifications are formulated as bilinear minimization problems whose variables are parameters included in piecewise linear Lyapunov functions and control gain matrices. The main result of this paper is to propose a method to solve bilinear programming problems so that the objective value at the obtained solution is in an /spl epsi/ neighborhood of the global optimal value.

Robust stabilization of control systems using piecewise linear Lyapunov functions and evolutionary algorithm

Piecewise linear Lyapunov functions are used to design control gain matrices so that closed systems are robustly stable and attractive regions are expanded as large as possible in given polytopic regions. The design problems for these specifications are formulated as bilinear programming problems whose constraints are divided into two groups, namely, linear inequalities and bilinear inequalities. In order to solve the constrained optimization problems, this paper presents a genetic algorithm that differs from traditional ones based on penalty techniques. The genetic algorithm starts from a feasible solution and retains its offspring, or population, within the feasible region. Besides the method creating such a starting point, several techniques are proposed to develop the diversity of population.