tailieunhanh - Optimal Control with Engineering Applications Episode 4

Tham khảo tài liệu 'optimal control with engineering applications episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 22 1 Introduction Exercises 1. In all of the optimal control problems stated in this chapter the control constraint Q is required to be a time-invariant set in the control space Rm. For the control of the forward motion of a car the torque T t delivered by the automotive engine is often considered as a control variable. It can be chosen freely between a minimal torque and a maximal torque both of which are dependent upon the instantaneous engine speed n t . Thus the torque limitation is described by Tmin n t T t Tmax n t . Since typically the engine speed is not constant this constraint set for the torque T t is not time-invariant. Define a new transformed control variable u t for the engine torque such that the constraint set Q for u becomes time-invariant. 2. In Chapter ten optimal control problems are presented Problems 1-10 . In Chapter 2 for didactic reasons the general formulation of an optimal control problem given in Chapter is divided into the categories and and and and and . Furthermore in Chapter a special form of the cost functional is characterized which requests a special treatment. Classify all of the ten optimal control problems with respect to these characteristics. 3. Discuss the geometric aspects of the optimal solution of the constrained static optimization problem which is investigated in Example 1 in Chapter . 4. Discuss the geometric aspects of the optimal solution of the constrained static optimization problem which is investigated in Example 2 in Chapter . 5. Minimize the function f x y 2x2 17xy 3y2 under the equality constraints x y 2 and x2 y2 4. 2 Optimal Control In this chapter a set of necessary conditions for the optimality of a solution of an optimal control problem is derived using the calculus of variations. This set of necessary conditions is known by the name Pontryagin s Minimum Principle 29 . Exploiting Pontryagin s Minimum Principle several optimal control problems are

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