Related papers: A note on first-order and transversality condition…
A class of infinite horizon optimal control problems involving mixed quasi-norms of $L^p$-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls. The…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
In this paper, we develop several necessary conditions of turnpike property for generalizaid linear-quadratic (LQ) optimal control problem in infinite dimensional setting. The term 'generalized' here means that both quadratic and linear…
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…
In this article, we prove second-order necessary optimality conditions for the so-called time crisis problem that comes up within the context of viability theory. It consists in minimizing the time spent by solutions of a controlled…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
We systematically introduce an approach to the analysis and (numerical) solution of a broad class of nonlinear unconstrained optimal control problems, involving ordinary and distributed systems. Our approach relies on exact representations…
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossible, to check. By taking advantage of several relaxations of…
The paper presents results about strong metric subregularity of the optimality mapping associated with the system of first-order necessary optimality conditions for a problem of optimal control of a semilinear parabolic equation. The…
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to…
This paper concerns a class of infinite horizon optimal control problems with state constraints. By extending the needle variation method to the infinite horizon case we obtain a complete set of necessary optimality conditions for a strong…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
In this paper we develop a Hamiltonian approach to sufficient conditions in optimal control problems. We extend the known conditions for $C^2$ maximised Hamiltonians into two directions: on the one hand we explain the role of a super…
In this paper, we consider a hierarchical control problem with model uncertainty. Specifically, we consider the following objectives that we would like to accomplish. The first one being of a controllability-type that consists of…
In this paper we consider an optimal control problem governed by a semilinear heat equation with bilinear control-state terms and subject to control and state constraints. The state constraints are of integral type, the integral being with…