SYSTEM IDENTIFICATION AND FILTERING OF NONLINEAR CONTROLLED MARKOV PROCESSES BY CANONICAL VARIATE ANALYSIS

CURRENT METHODS FOR SYSTEM IDENTIFICATION FOR NONLINEAR MARKOV PROCESSES ARE RESTRICTED TO VERY SPECIAL FORMS OR PROVIDE POOR APPROXIMATIONS TO OPTIMAL PROCEDURES. THE OBJECTIVE OF THE PHASE I RESEARCH IS TO DEMONSTRATE THE TECHNICAL FEASIBILITY OF USING STATE AFFINE MARKOV PROCESSES AND CANONICAL VARIATE ANALYSIS (CVA) FOR OBTAINING APPROXIMATIONS TO OPTIMAL NONLINEAR PROCEDURES FOR SYSTEM IDENTIFICATION AND STOCHASTIC FILTERING. A RIGOROUS DEVELOPMENT OF THE HILBERT SPACE THEORY FOR APPROXIMATION OF NONLINEAR CONTROLLED MARKOV PROCESSES BY STATE SPACE AFFINE MODELS AND BY CANNONICAL VARIATE ANALYSIS IS PROPOSED. FINITE DIMENSIONAL STATE AFFINE MODELS OBTAINED BY TRUNCATION OF THE INFINITE DIMENSIONAL CVA WILL BE USED TO DERIVE PRACTICAL COMPUTATIONAL ALGORITHMS FOR APPROXIMATION OF OPTIMAL SYSTEM IDENTIFICATION AND STOCHASTIC FILTERS FOR NONLINEAR SYSTEMS. THE PERFORMANCE OF THESE COMPUTATIONAL ALGORITHMS WILL BE DEMONSTRATED USING A COMPUTER SIMULATION OF A NONLINEAR AEROSPACE SYSTEM. IN PHASE II, THE FULL MATHEMATICAL THEORY WILL BE ELABORATED, DETAILED COMPUTATIONAL AND NUMERICAL ALGORITHMS WILL BE DERIVED, AND COMMERCIAL GRADE SOFTWARE WILL BE DEVELOPED AND DEMONSTRATED ON A FULL SCALE AEROSPACE PROBLEM.