On time optimal control of integrator switched systems with state constraints

In this paper, time optimal control problems of a class of integrator switched systems with polyhedral state constraint subsets are studied. We first develop a directed graph representation of the system discrete structure. Based on the graph representation, we generate candidate solution paths and propose an algorithm for seeking the optimal solution. A linear programming method for finding the optimal timing information for each path is then proposed. Finally, we report preliminary results on some sufficient conditions and techniques which help reduce the number of candidate paths.     

On optimal control problems with state constraints

This paper is concerned with necessary conditions for a general optimal control problem developed by Russak and Tan. It is shown that, in most cases, a further relation between the multipliers holds. This result is of interest in particular for the investigation of perturbations of the state constraint.     

Optimal control problems with state constraints for semilinear distributed-parameter systems

We consider optimal control problems for distributed-parameter systems described by semilinear equations, with constraints on the control and on the state, and an exact pointwise target condition. As an application of a general theory of nonlinear programming problems in Banach spaces, a version of the Pontryagin maximum principle is obtained.This research was partly supported by the National Science Foundation under Grant DMS-92-21819.     

On some elliptic optimal control problems with state constraints

In this paper optimality conditions will be derived for elliptic optimal control problems with a restriction on the state or on the gradient of the state. Essential tools are the method of transposition and generalized trace theorems and green's formulas from the theory of elliptic differential equations.     

Internal approximations of reachable sets of control systems with state constraints

We construct self-intersecting flexible cross-polytopes in the spaces of constant curvature, that is, in Euclidean spaces \(\mathbb{E}^n\) , spheres \(\mathbb{S}^n\) , and Lobachevsky spaces Λ ⁿ of all dimensions n. In dimensions n ≥ 5, these are the first examples of flexible polyhedra. Moreover, we classify all flexible cross-polytopes in each of the spaces \(\mathbb{E}^n\) , \(\mathbb{S}^n\) , and Λ ⁿ . For each type of flexible cross-polytopes, we provide an explicit parametrization of the flexion by either rational or elliptic functions.     

Feedback approximation of the minimum energy control for linear infinite-dimensional systems with zero terminal state

The paper studies the minimum energy control problem for linear infinite-dimensional systems with an unbounded input operator and zero terminal state. This problem is approximated by the minimum energy control problem with a small terminal state for which the solution is derived in feedback form. The operators which comprise the feedback are described in terms of differential relations which, depending on circumstances, involve Liapunov or Riccati differential equations. A detailed example illustrates how the general results apply to the wave equation with control in Dirichlet boundary condition.This work was supported by the Polish Ministry of National Education under Grant DNS-T/02/097/90-2.     

Optimal control of infinite-dimensional uncertain systems

In this paper, we consider a minimax problem of optimal control for a class of strongly nonlinear uncertain evolution equations on a Banach space. We prove the existence of optimal controls. A nontrivial example of a class of systems governed by a nonlinear partial differential equation with uncertain spatial parameters is presented for illustration.This work was supported in part by the National Science and Engineering Research Council of Canada under Grant No. A7109 and The Engineering Faculty Development Fund, University of Ottawa.The authors would like to thank the anonymous reviewers for their valuable comments and suggestions.     

Computational method for optimal control of switched systems with input and state constraints

In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standard optimization techniques. In addition, although conjugate gradient algorithms are very useful for solving nonlinear optimization problem, in practical implementations, the existing Wolfe condition may never be satisfied due to the existence of numerical errors. And the mode insertion technique only leads to suboptimal solutions, due to only certain mode insertions being considered. Thus, based on an improved conjugate gradient algorithm and a discrete filled function method, an improved bi-level algorithm is proposed to solve this optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Three numerical examples are solved to illustrate the proposed algorithm converges faster and yields a better cost function value than existing bi-level algorithms.     

Representation of infinite-dimensional neutral non-autonomous control systems

This paper studies the well-posedness of a class of non-autonomous neutral control systems in Banach spaces. We prove that such systems are represented by absolutely regular non-autonomous linear systems in the sense of Schnaubelt [R. Schnaubelt, Feedback for non-autonomous regular linear systems, SIAM J. Control Optim. 41 (2002) 1141-1165]. This paper can be considered as the non-autonomous version of the work presented in [H. Bounit, S. Hadd, Regular linear systems governed by neutral FDEs, J. Math. Anal. Appl. 320 (2006) 836-858].     

Sufficient conditions for optimal control with state and control constraints

A monotonicity result is utilized to derive sufficient optimality conditions of considerable generality for an individual trajectory in control theory. The sufficiency theorem embodying these conditions generalizes those of Boltyanskii and Leitmann and is applied to a simple control system to which their sufficiency theorems are not applicable. Conditions on the state equations and state space are completely relaxed. The set of admissible controls is extended to the set of measurable controls and the integrand of the performance index has its membership extended to the class of bounded Borel-measurable functions. The decomposition of the state space is required to be onlyplain denumerable.     

Boundary optimal flow control with state constraints

The numerical solution of the Dirichlet boundary optimal control problem of the Navier-Stokes equations in presence of pointwise state constraints is investigated. A Moreau-Yosida regularization of the problem is proposed to obtain regular multipliers. Optimality conditions are derived and the convergence of the regularized solutions towards the original one is presented. The paper ends with a numerical experiment. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal feedback control for dynamic systems with state constraints: An exact penalty approach

In this paper, we consider a class of nonlinear dynamic systems with terminal state and continuous inequality constraints. Our aim is to design an optimal feedback controller that minimizes total system cost and ensures satisfaction of all constraints. We first formulate this problem as a semi-infinite optimization problem. We then show that by using a new exact penalty approach, this semi-infinite optimization problem can be converted into a sequence of nonlinear programming problems, each of which can be solved using standard gradient-based optimization methods. We conclude the paper by discussing applications of our work to glider control.     

On observability and stability in infinite-dimensional linear systems

It seems to be generally known (Ref. 1) that, in the case of finite-dimensional systems, the state stability properties of the system may be inferred from the output stability properties if the system is completely observable.In the case of infinite observable systems, the notion of observability generalizes in two distinct ways, weak and strong notions. The above-mentioned stability properties remain true only for the case of strong observability.This research was partially supported by the Bat-Sheva de Rothschild Fund for Advancement of Science and Technology.     

On strong controllability of infinite-dimensional linear systems

If an infinite-dimensional linear system is strongly controllable (i.e., every state can be reached from any state in finite time), then it is strongly controllable in uniform finite time.     

On the controllability of infinite-dimensional linear systems

Two types of controllability, namely weak controllability and strong controllability, are defined for general linear systems. Both types of controllability are useful in control theory. If the system is finite-dimensional, the two types of controllability are equivalent to each other and to the standard concept of complete state-controllability.     

Optimal impulsive control problems with state and mixed constraints

Doklady Mathematics -     

Elliptic operators with infinite-dimensional state spaces

Motivated by applications to problems from physics, we study elliptic operators with operator-valued coefficients acting on Banach-space-valued distributions. After giving a definition of ellipticity, normal ellipticity in particular, generalizing the classical concepts, we show that normally elliptic operators are negative generators of analytic semigroups on for 1 and on and , as well as on all Besov spaces of E-valued distributions on , where E is any Banach space. This is true under minimal regularity assumptions for the coefficients, thanks to a point-wise multiplier theorem for E-valued distributions proven in the appendix. Received August 23, 2000; accepted December 12, 2000.     

On the optimal control of linear systems with linear performance criterion and constraints

We suggest an analytical-numerical method for solving a boundary value optimal control problem with state, integral, and control constraints. The embedding principle underlying the method is based on the general solution of a Fredholm integral equation of the first kind and its analytic representation; the method permits one to reduce the boundary value optimal control problem with constraints to an optimization problem with free right end of the trajectory.