doc. Ing. Petr Hušek, Ph.D.

Fuzzy logic inherently enables incorporating of a prior knowledge about the system into the identification algorithms of nonlinear dynamic systems using measured input-output data, a process that is called grey-box modelling. A prior knowledge is often available from physical grounds, e.g. exact knowledge of steady-state input-output characteristics, its monotonicity, monotonicity of step response, approximate knowledge of partial derivatives of the outputs along the particular inputs or other qualitative properties that are either global or valid only in some regions or for particular inputs. Nevertheless, it is not easy to incorporate such a rough knowledge usually described linguistically into the analytical formulas of black-box identification. State of the art: In the past there were few attempts to incorporate the monotonicity condition for multi-input mapping corresponding to Mamdani fuzzy logic. Unfortunately, usability of all the algorithms is restricted to a special choice of membership functions and the derived conditions are very conservative that results in poor approximation capability of fuzzy mapping. A simple and intuitive result for membership functions with finite support telling that monotonicity with respect to all inputs is enforced if both input and output membership functions are ordered in the same manner was presented in [1]. In [2] monotonicity conditions were derived for Gaussian input membership functions with the same variance and in [3] it was proven that such a system is universal approximator of monotonic functions. The conditions were used for ensuring monotonicity of steady-state input-output characteristics for some applications in [4]. In [5] conditions for convexity of single-input single-output fuzzy mapping with triangular input membership functions were derived and their universal approximation ability of convex functions was proven at the same time.

The main goal of the thesis is to develop algorithms for reinforcement learning (RL) based control of dynamical systems that will use prior knowledge. Even though RL typically works without any prior knowledge about the controlled system or about the optimal policy, certain amount is often available and its utilization can be very beneficial since it may significantly reduce computational complexity of RL algorithms. Prior knowledge can refer e. g. to the policy, to the value function or to the system dynamics. Considered possibilities of prior information will be especially monotonicity of the policy with respect to some or all state variables and convexity of Q-function with respect to to some or all state and action variables. Considered tools for Q-function and policy iteration approximations will be fuzzy systems and neural networks, both multilayer perceptrons and radial basis function networks with different kernels.

Despite the progress in development of advanced control methods PID controllers remain explicitly the most used controllers for technological processes at the lowest level especially due to their simple realization and ability to achieve satisfactory behaviour for stable nonoscillatory or overdamped systems with small transport delay. Even though the structure is simple their tuning is a complicated procedure even for SISO systems. Unfortunately, the existing tuning algorithms for MIMO systems, even if with great application potential, do not consider robustness or disturbance attenuation or even do not guarantee stability. The research topics include: design of decentralized PID controllers guaranteeing closed-loop performance, design involving decoupling with respect to robustness and disturbance attenuation and development of adaptive algorithms based on closed-loop identification. The candidates should have a solid background in control systems theory.