سجاد پاك خصال

Nonlinear time-varying systems are a kind of dynamic systems that have been less studied and many methods in control theory have not been developed for them. Approximate dynamic programming is an iterative method that employed to solve many problems including the design of optimal and H∞ controllers for dynamic systems. One of the family of approximate dynamic programming algorithms are policy iteration algorithms, which are more useful in solving control problems due to their structural features. In policy iteration algorithms, data-based methods in artificial intelligence are usually used to approximate the cost function and improve the control policy based on it. However, in the case of time-varying systems, the dependence of the cost function on time, which is a continuous and unlimited variable, makes it difficult to use data-based methods. In this thesis, the topic of using the sum-of-squares optimization-based policy iteration algorithms for optimal control and H∞ control of nonlinear time-varying systems is studied. First, a policy iteration algorithm for suboptimal control of polynomial time-varying systems is presented. The convergence of this iterative algorithm and the stability of the resulting closed-loop system will also be proved. In the policy eva‎luation step of the presented algorithm, a sum of squares optimization problem should be solved. The existence of this optimization problem has made it possible to add constraints to guarantee exponential stability and guarantee the positivity of the Lyapunov function. Then, a sum-of-squares optimization-based policy iteration algorithm is presented for H∞ control of nonlinear time-varying systems with external disturbance inputs and uncertain parameters with known bounds. In the H∞ control, the goal is to design a controller that stabilizes the system in the absence of disturbance and, in its presence, makes the system L2-gain under a prescribed level of disturbance attenuation. This prescribed value is called the disturbance attenuation coefficient. In this thesis, a systematic method is also presented to achieve a policy that can guarantee a smaller disturbance attenuation coefficient. The convergence of the policy iteration algorithm, the global exponential stability and the H∞ performance are also proved for all possible values of the uncertain parameters. Also, in order to verify the effectiveness of the proposed algorithms, examples with numerical simulations are provided in each chapter.

كنترل بهينه , كنترل مقاوم , برنامه‌ريزي پوياي تقريبي , الگوريتم تكرار سياست , سيستم‌هاي متغير با زمان , برنامه‌ريزي مجموع مربعات

Optimal control , robust control , approximate dynamic programming , policy iteration algorithm , time-varying systems , sum-of-squares programming

sajjad pakkhesal

saeed shamaghdari