Abstract— In this paper, a computational method for solving constrained nonlinear optimal control problems is presented with an application to the container crane. The method is based on Banks' et al. iterative approach, in which the nonlinear system state equations are replaced by a sequence of time-varying linear systems. Therefore, The constrained nonlinear optimal control problem can be con...

Primal and dual problems of optimal control with linear, quadratic or piecewise linear-quadratic convex objective are considered in which a linear dynamical system is subjected to linear inequality constraints that could jointly involve states and controls. It is shown that when such constraints, except for the ones on controls only, are represented by penalty terms, and a mild coercivity condi...

In previous lectures, we discussed the design of state feedback controllers using using eigenvalue (pole) placement algorithms. For single input systems, given a set of desired eigenvalues, the feedback gain to achieve this is unique (as long as the system is controllable). For multi-input systems, the feedback gain is not unique, so there is additional design freedom. How does one utilize this...

In this paper we solve the basic fractional analogue of the classical linear-quadratic Gaussian regulator problem in continuous-time with partial observation. For a controlled linear system where both the state and observation processes are driven by fractional Brownian motions, we describe explicitly the optimal control policy which minimizes a quadratic performance criterion. Actually, we sho...

Inspired by the successes of stochastic algorithms in training deep neural networks and simulation interacting particle systems, we propose analyze a framework for randomized time-splitting linear-quadratic optimal control. In our proposed framework, linear dynamics original problem is replaced dynamics. To obtain dynamics, system matrix split into simpler submatrices time interval interest sub...