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 ...

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 ...

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...

The problem associated with trajectory generation for a car-like robot (CLR) moving from an initial configuration to any final configuration is studied in this paper. The aim of our research is to achieve energy-optimal solution to the problem of trajectory generation. Based on bang-bang control theory, the necessary condition for energy-optimal trajectory generation is studied. Based on steeri...

classical control methods such as pontryagin maximum principle and bang-bang principle and other methods are not usually useful for solving opti-mal control systems (ocs) specially optimal control of nonlinear systems (ocns). in this paper, we introduce a new approach for solving ocns by using some combination of atomic measures. we define a criterion for controllability of lumped nonlinear con...

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...

The problem of maintaining acceptable performance of a perturbed control system under conditions of feedback failure is considered. The objective is to maximize the time during which performance remains within desirable bounds without feedback, given that the parameters of the controlled system are within a specified neighborhood of their nominal values. It is shown that there is an optimal ope...

At present, many metropolitan sewer systems do not meet existing and proposed standards on water pollution. Existing systems were designed to overflow at prescribed locations in order to protect the sewage treatment plants whenever severe overload conditions exist (usually during storms). This discharge of untreated overflows into natural receiving waters is of growing concern to water pollutio...