We consider the optimal control of feedback linearizable dynamic systems subject to mixed state and control constraints. The optimal controller is allowed to be discontinuous including bang-bang control. Although the nonlinear system is assumed to be feedback linearizable, in general, the optimal control does not linearize the dynamics. The continuous optimal control problem is discretized usin...

We focus on the minimal time control problem for single-input control-affine systems ẋ = X(x) + u1Y1(x) in IR with fixed initial and final time conditions x(0) = x̂0, x(t f ) = x̂1, and where the scalar control u1 satisfies the constraint |u1(·)| 6 1. For these systems a concept of conjugate time tc has been defined in e.g. [3, 30, 33] in the bang-bang case. Besides, theoretical and practical iss...

This paper studies the bang-bang property for time optimal controls governed by semilinear heat equation in a bounded domain with control acting locally in a subset. Also, we present the null controllability cost for semilinear heat equation and an observability estimate from a positive measurable set in time for the linear heat equation with potential.

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 article studies the time-optimal output transition problem to change the system output, from an initial value y(t) = y (for all time t ≤ 0) to a final value y(t) = y (for all time t ≥ T ), for invertible nonlinear systems. The main contribution of the article is to show that the use of preand post-actuation input outside the transition interval IT = [0, T ] can reduce the transition time T...

The design of robust time-optimal controllers using the sensitivity concept is presented in this paper. A parameter optimization problem is solved using the Switch Time Optimization algorithm to determine a bang-bang control profile that minimizes the maneuver time subject to the constraint that the sensitivity of the final states with respect to system parameters are zero. The proposed approac...

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...

In this paper, we propose a new fuzzy bang–bang relay controller (FBBRC). The bang–bang control systems use switching relays or hard limiter saturation functions with fixed parameters, and their input does not have the flexibility to control the non-linear system over its entire range of operation. The conventional fuzzy bang–bang controllers have an analog output and an external hard limiting ...

The synthesis of time-optimal feedback control of a single input, continuous time, linear time invariant system with bounded inputs is considered. Unlike a recent paper by the authors, the target final state is not necessarily the origin of the state space. Semi-algebraic representations of switching surfaces corresponding to the bang-bang time-optimal control are computed using a Gröbner basis...

This paper addresses the problem of time-optimal motions for a mobile platform in a planar environment. The platform has two non-steerable independently driven wheels. The overall mission of the robot is expressed in terms of a sequence of via points at which the platform must be at rest in a given configuration (position and orientation). The objective is to plan time-optimal trajectories betw...