Approximate dynamic programming based solutions for fixed-final-time optimal control and optimal switching

Optimal solutions with neural networks (NN) based on an approximate dynamic programming (ADP) framework for new classes of engineering and non-engineering problems and associated difficulties and challenges are investigated in this dissertation. In the enclosed eight papers, the ADP framework is utilized for solving fixed-final-time problems (also called terminal control problems) and problems with switching nature. An ADP based algorithm is proposed in Paper 1 for solving fixed-final-time problems with soft terminal constraint, in which, a single neural network with a single set of weights is utilized. Paper 2 investigates fixed-final-time problems with hard terminal constraints. The optimality analysis of the ADP based algorithm for fixed-final-time problems is the subject of Paper 3, in which, it is shown that the proposed algorithm leads to the global optimal solution providing certain conditions hold. Afterwards, the developments in Papers 1 to 3 are used to tackle a more challenging class of problems, namely, optimal control of switching systems. This class of problems is divided into problems with fixed mode sequence (Papers 4 and 5) and problems with free mode sequence (Papers 6 and 7). Each of these two classes is further divided into problems with autonomous subsystems (Papers 4 and 6) and problems with controlled subsystems (Papers 5 and 7). Different ADP-based algorithms are developed and proofs of convergence of the proposed iterative algorithms are presented. Moreover, an extension to the developments is provided for online learning of the optimal switching solution for problems with modeling uncertainty in Paper 8. Each of the theoretical developments is numerically analyzed using different real-world or benchmark problems --Abstract, page v

Robust Model Based Control of Constrained Systems.

This dissertation is concerned with control of systems subject to input and state constraints. Model Predictive Control (MPC) is one promising control technique that is capable of dealing with constraints. Its flexible formulation also provides mechanisms to tune the closed loop system for desired performance. However, due to computational complexity and its dependency on accurate models of the system, the MPC applications for systems with fast dynamics or with model uncertainties are not wide spread. The focus of this dissertation is to develop methodologies and tools that can enhance the computational efficiency and address robustness issues of constrained dynamic systems. The core contribution of this dissertation is that it provides a computational efficient MPC solver, referred to as InPA-SQP (Integrated Perturbation Analysis and Sequential Quadratic Programming). The main results include four major components. First, a neighboring extremal control method is proposed for discrete-time optimal control problems subject to a general class of inequality constraints. A closed form solution for the neighboring extremal (NE) control is provided and a sufficient condition for existence of the neighboring extremal solution is specified. Second, the NE method is integrated with sequential quadratic programming that leads to InPA-SQP. Third, a robust control method is introduced for linear discrete-time systems subject to mixed input-state constraints. Unlike conventional MPC, the method does not require repeatedly solving an optimization problem online while guarantees states convergence to a minimal invariant set. Fourth, it is shown that if the dynamics of disturbances are incorporated, the attractor set associated with the proposed constrained robust control methods can be considerably smaller, leading to a much less conservative design. Applications of the InPA-SQP and proposed constrained robust control constitute the other key element of the study. The InPA-SQP is employed in two experimental applications: one for voltage regulation of a DC/DC converter and another for path following of a model ship. Both applications show effectiveness of the method in terms of computation and constraints handling. These applications not only serve as validation platforms but also motivate new research topics for further investigation.Ph.D.Electrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/77854/1/ghaemi_1.pd