Shaping

Abstract: It is shown that the successive approximation procedure simplifies computations of the optimal solution of a bilinear-quadratic optimal control problem. On the contrary to the results of Hofer and Tibken (1985) where the optimal solution has been obtained in terms of a sequence of the differential Riccati equations, in the presented method only solutions of a sequence of the differential Lyapunov equations are required. A chemical reactor example is used to demonstrate the efficiency of the new method. >

Abstract: Introduction The viewpoint adopted for experimental purposes in this study was that the behavior of an organism is generated and maintained chiefly by its consequences on the environment. Over a wide range of conditions, a hungry rat, placed in a so-called "Skinner box," will persist in pressing a bar if, as a consequence of this response, a pellet of food is delivered to it at least some of the time. This exemplifies the principle of reinforcement which is at the core of current behavior theory. Conditioning of this type is termed operant (instrumental) to distinguish it from respondant (classical Pavlovian) conditioning. The probability of a given response in relation to the conditions of reinforcement of that response has been the subject of much study of Skinner, 4 Ferster and Skinner, 2 an others. Recently, controlled experiments conducted with human subjects using cubicles analogous to the

Abstract: The paper contains a survey of results devoted to one of the numerical methods of optimal control—the method of successive approximations. This method is based on Pontryagin's maximum principle and is known in the English literature as the min-H method. Various modifications of the method and some theoretical results on its convergence are presented. Examples of applications of the method for the calculation of optimal trajectories are given. The method of small parameters which is close to the method of successive approximations, is also described.