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Reinforcement Learning and Approximate Dynamic Programming for Feedback Control

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Modern day society relies on the operation of complex systems including aircraft, automobiles, electric power systems, economic entities, business organizations, banking and finance systems, computer networks, manufacturing systems, and industrial processes, Decision and control are responsible for ensuring that these systems perform properly and meet prescribed performance objectives, The safe, reliable, and efficient control of these systems is essential for our society, Therefore, automatic decision and control systems are ubiquitous in human engineered systems and have had an enormous impact on our lives. As modern systems become more complex and performance requirements more stringent, improved methods of decision and control are required that deliver guaranteed performance and the satisfaction of prescribed goals.

Feedback control works on the principle of observing the actual outputs of a system, comparing them to desired trajectories, and computing a control Signal based on that error, which is used to modify the performance of the system to make the actual output follow the desired trajectory. The optimization of sequential decisions or controls that are repeated over time arises in many fields, including artificial intelligence, automatic control systems, power systems, economics, medicine, operations research, resource allocation, collaboration and coalitions, business and finance, and games including chess and backgammon. Optimal control theory provides methods for computing feedback control systems that deliver optimal performance. Optimal controllers optimize user-prescribed performance functions and are normally designed offline by solving Hamilton-Jacobi-Bellman (HJB) design equations. This requires knowledge of the full system dynamics model. However, it is often difficult to determine an accurate dynamical model of practical systems. Moreover, determining optimal control policies for nonlinear systems requires the offline solution of nonlinear HJB equations, which are often difficult or impossible to solve. Dynamic programming (DP) is a sequential algorithmic method for finding optimal solutions in sequential decision problems. DP was developed beginning in the 1960s with the work of Bellman and Pontryagin. DP is fundamentally a backwards-in-time procedure that does not offer methods for solving optimal decision problems in a forward manner in real time.
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