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In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
An analysis of the motion of a relativistic electron under a linear constraint in four dimensions is presented. Interesting results are given that show that the state of the electron is well defined under the formalism of time optimal…
We study local structure of time-optimal controls and trajectories for a 3-dimensional control-affine system with a 2-dimensional control parameter with values in the disk. In particular, we give sufficient conditions, in terms of Lie…
This paper presents an approach to damp out the oscillatory motion of the pendulum-like hanging platform on which a robotic manipulator is mounted. To this end, moving masses were installed on top of the platform. In this paper, asymptotic…
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
An application of optimal control theory results in a lower bound on the speed $|\dot{\lambda}(t)|$ that must be attained at least once by any external forcing function that induces tipping in the asymptotically autonomous scalar ODE…
We present the conditions under which the time-optimal control problem for a nonlinear non-autonomous linearizable system can be solved by the method of successive approximations, at each step of which a power Markov moment min-problem is…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…
The positive-real and bounded-real lemmas solve two important linear-quadratic optimal control problems for passive and non-expansive systems, respectively. The lemmas assume controllability, yet a passive or non-expansive system can be…
We apply an extension of the Pontryagin Maximum Principle to derive time-optimal controls of two-level quantum systems by means of piecewise constant pulses. Global optimal solutions are obtained for state-to-state transfer in the cases…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
The paper is concerned with a general optimization problem for a nonlinear control system, in the presence of a running cost and a terminal cost, with free terminal time. We prove the existence of a patchy feedback whose trajectories are…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal…
We study a time minimization problem on the group of motions of a plane with admissible control in a half-disk. The considered control system describes a model of a car that can move forward on a plane and turn in place. Optimal…
We deduce stability results for finite control set and mixed-integer model predictive control with a downstream oversampling phase. The presentation rests upon the inherent robustness of model predictive control with stabilizing terminal…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…