We consider Euler discretizations to a class of linear-quadratic optimal control problems. Assuming that the discrete controls are of bang-bang type and define switching functions with a uniform structure independent of the discretization we show, that the discrete controls converge to a bang-bang control, which is a solution of the original problem.

Second order sufficient optimality conditions for bang-bang control problems in a very general form have been obtained in [15, 21, 13, 12, 1]. These conditions require the positive definiteness (coercivity) of an associated quadratic form on the finite-dimensional critical cone. In the present paper, we investigate similar conditions for optimal control problems with a control variable having t...

A new fuzzy bang–bang relay controller (FBBRC) is introduced in this paper. The new controller is inherently optimal due to its bang–bang property. The controller has fuzzy decision-making capability in its inputs and have two fixed levels bang–bang output. Consequently, the tuning of FBBRC is restricted to input parameters only in comparison to standard fuzzy logic controller (FLC) where the o...

Rapid state control of quantum systems is significant in reducing the influence of relaxation or decoherence caused by the environment and enhancing the capability in dealing with uncertainties in the model and control process. Bang-bang Lyapunov control can speed up the control process, but cannot guarantee convergence to a target state. This paper proposes two classes of new Lyapunov control ...

Second order necessary and sufficient optimality conditions for bang–bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi–)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadr...

A multigrid scheme for the solution of constrained optimal control problems discretized by finite differences is presented. This scheme is based on a new relaxation procedure that satisfies the given constraints pointwise on the computational grid. In applications, the cases of distributed and boundary control problems with box constraints are considered. The efficient and robust computational ...

For stabilization of a robot manipulator upon collision with a stiff environment, a nonlinear bang-bang impact controller is developed. Under this control, a robot can successfully achieve contact tasks without changing control algorithm or controller gains throughout all three modes: free space, transition and constrained motion. It uses a robust hybrid impedance/time-delay control algorithm t...

This paper deals with the optimal control problem that arise when a hydraulic system with fixed-head hydroplants is considered. In the frame of a deregulated electricity market the resulting Hamiltonian for such systems is linear in the control variable and results in an optimal singular/bang-bang control policy. To avoid difficulties associated with the computation of optimal singular/bang-ban...

This note proposes a model predictive control (MPC) algorithm for the solution of a robust control problem for continuous-time systems. Discontinuous feedback strategies are allowed in the solution of the min–max problems to be solved. The use of such strategies allows MPC to address a large class of nonlinear systems, including among others nonholonomic systems. Robust stability conditions to ...

We investigate two well-known basic optimal control problems for chemotherapeutic cancer treatment modified by introducing a timedependent “resistance factor”. This factor should be responsible for the effect of the drug resistance of tumor cells on the dynamical growth for the tumor. Both optimal control problems have common pointwise but different integral constraints on the control. We show ...