Robust control algorithms for Markovian jumping parameters: application to flexible manufacturing systems

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Modern control systems must meet performance requirements and maintain acceptable behavior even in the presence of abrupt changes in their dynamic due, for instance, to random component failures or repairs. Sys- tems with this behavior may be modelled as hybrid ones, that is, to the continuous state variable, a discrete random variable called the mode, or regime is appended. The mode describes the random jumps of the system parameters and the occurrence of the discontinuities. One of the most important hybrid class of systems is the one called Markovian jumping systems (MJS), in which the mode-process is a continuous-time discrete-state Markov process taking values in a finite set. Flexible manufacturing systems (FMS) are a good example of this class of systems and they constitute at the present time, the technologically most sophisticated production tool in manufacturing. FMS constitue an important engineering and mathematical challenge in view of a combina- tion of complex features: flexibility, large scale interconnected systems, random events such as machine failu- res, operator absence and fluctuating markets, etc. This combination of difficulties is what we wish to address in the present research proposal for the application part, with the conviction that the development of a systema- tic planning and scheduling methodology for FMS could improve productivity, significantly enhance the com- petitivity of Canada on international markets. My objectives in this research proposal are: 1. Theory: develop robust algorithms for control and estimation for the class of systems with MJS (linear, linear with time delay, nonlinear) in the presence of uncertainties; 2. Application: develop robust production and maintenance (correc- tive and preventive) scheduling algorithms and propose numerical methods to solve the corresponding optimality conditions. Use the infenitesimal perturbation analysis to estimate the optimal threshold value for the flow control problem in FMS. Adapt the formalism of adaptive control for FMS. The methodology I use in this research proposal is the one used in control theory and optimization, which includes deterministic and stochastic optimal control, hierarchical control, stochastic dynamic programming and game theory.