Rizk, Charbel George.

The problem at hand is developing a controller design methodology that is generally applicable to autonomous systems with fairly accurate models. The controller design process has two parts: synthesis and analysis. Over the years, many synthesis and analysis methods have been proposed. An optimal method for all applications has not yet been found. Recent advances in computer technology have made computational methods more attractive and practical. The proposed method is an iterative computational method that automatically generates non-linear controllers with specified global performance. This dissertation describes this method which consists of using an analysis tool, continued propagation cell mapping (CPCM), as feedback to the synthesis tool, best estimate directed search (BEDS). Optimality in the design can be achieved with respect to time, energy, and/or robustness depending on the performance measure used. BEDS is based on a novel search concept: globally directing a random search. BEDS has the best of two approaches: gradient (or directed) search and random search. It possesses the convergence speed of a gradient search and the convergence robustness of a random search. The coefficients of the best controller at the time direct the search process until either a better controller is found or the search is terminated. CPCM is a modification of simple cell mapping (SCM). CPCM maintains the simplicity of SCM but provides accuracy near that of a point map (PM). CPCM evaluates the controller's complete and global performance efficiently and with easily tunable accuracy. This CPCM evaluation guarantees monotonic progress in the synthesis process. The method is successfully applied to the design of a TSK-type fuzzy logic (FL) controller and a Sliding Mode-type controller for the uncertain non-linear system of an inverted pendulum on a cart for large pole angles (+/-86 degrees). The resulting controller's performance compares favorably to other established methods designed with dynamic programing (DP) and genetic algorithms (GA). When CPCM is used as feedback to BEDS, the resulting design method quickly and automatically generates non-linear controllers with good global performance and without much a priori information about the desired control actions.