Adaptive optimal regulation of the Canadian economy using optimal control theory. by Honkan Lau Download PDF EPUB FB2
For analysing the stochastic optimal control problem under varying degrccs. of uncertainty to apply the algorithms to a relatively-small, econornetr ic model of the Canadian economy to assess the practical applications of stochastic optimal control theory. He is with the Control and Estimation Tools development team at The MathWorks, Inc.
His research interest is in the areas of nonlinear control, optimal control, neural network control, and adaptive intelligent systems.
He is the author/co-author of one book, two book chapters, 13 journal papers and 17 refereed conference by: Optimal control theory provides a powerful and efficient method of deriving rules which will enable a dynamic system to be held to a preferred path.
This makes it appear at first sight eminently suitable to be used as a tool to assist economic policymakers in their task of improving the performance of the : Penelope A. Rowlatt. In this paper we propose a new scheme based on adaptive critics for finding online the state feedback, infinite horizon, optimal control solution of linear continuous-time systems using only partial knowledge regarding the system dynamics.
In other words, the algorithm solves online an algebraic Riccati equation without knowing the internal dynamics model of the system. optimal control theory have proved to be more productive in the analysis of optimality conditions in mathematical economics and not in the computation of optimal trajectories in econometric models.
Keywords: Optimal Control Theory, Stochastic Control, Adaptive Control, Economic Applications. JEL Classification: C54, C61, E61 1. IntroductionCited by: 1. Recent economic applications of optimal and adaptive control theory have increased our understanding of the meaning of optimality in a dynamic horizon e.g., the shadow prices or adjoint variables along the optimal trajectory, their stability properties and the implications of.
Optimal control theory (Stengel, ) answers this question by postulating that a particular choice is made because it is the optimal solution to the task. Most optimal motor control models so far have fo-cused on open loop optimisation in which the se-quence of motor commands or the trajectory is di.
Abstract: This note studies the adaptive optimal output regulation problem for continuous-time linear systems, which aims to achieve asymptotic tracking and disturbance rejection by minimizing some predefined costs.
Reinforcement learning and adaptive dynamic programming techniques are employed to compute an approximated optimal controller using input/partial-state. theory of optimal control processes, decision theory, and the theory of games.
This dissertation therefore attempts (l) to develop concepts that will be useful tools in describing the economic policy problem, (11) to describe the problem mathe matically, and (ill) to develop some methods of approaching. the complex biophysical, social-economic-political systems in the region would require an increased emphasis on new knowledge.
As a result, it called for adop-tion of an adaptive management strategy to gain new understanding. It proposed a four-phase adaptive management cycle (ﬁg. In the ﬁrst phase, plans are framed. In contrast, optimal control theory focuses on problems with continuous state and exploits their rich di⁄erential structure.
2 Continuous control: Hamilton-Jacobi-Bellman equations We now turn to optimal control problems where the state x 2Rnx and control u 2U(x) Rnu are real-valued vectors. To simplify notation we will use the shortcut min u. These issues can again be handled through suitable control theoretic models that recognize spatial linkages between economic systems.
In this special issue of OCAM, we have provided a selection of articles that address some of these issues using optimal control techniques. The goal is to provide an overview of some of the important topics being.
Optimal control theory is formulated in continuous time, though there is also a discrete time version of the maximum principle; see Léonard and Long (). In discrete time, the most commonly used optimization technique is dynamic programming, developed by Bellman (), using a recursive method based on the principle of optimality.
4 CHAPTER 1. INTRODUCTION TO OPTIMAL CONTROL One of the real problems that inspired and motivated the study of optimal control problems is the next and so called \moonlanding problem".
Example The moonlanding problem. Consider the problem of a spacecraft attempting to make a soft landing on the moon using a minimum amount of fuel. Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain.
For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to.
Which brings us to the Adaptive Control of Thought, or ACT-R. The Adaptive Control of Thought is a learning theory created by Canadian Psychologist John Anderson and explored, among other places, in his publication, ‘How Can the Human Mind Occur in the Physical Universe?’ (The ‘R’ stands for ‘Rational’–see Anderson, J.
Initially, optimal control theory foundits application mainly in engi-neering disciplines like aeronautics, chemical and electrical engineering, robotics. In the later decades it has found more and more applications in economic theory and computational nance, e.
in macroeconomic growth theory, microeconomic theory of rm and consumer as well. Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in both science and engineering.
For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the.
Optimal Control theory has been increasingly used in Economi- and Management Science in the last fifteen years or so. It is now commonplace, even at textbook level. It has been applied to a great many areas of Economics and Management Science, such as Optimal Growth, Optimal Population, Pollution.
The book shows how ADP can be used to design a family of adaptive optimal control algorithms that converge in real-time to optimal control solutions by measuring data along the system trajectories.
Generally, in the current literature adaptive controllers and optimal controllers are two distinct methods for the design of automatic control systems.
ECON Optimal Control Theory 6 3 The Intuition Behind Optimal Control Theory Since the proof, unlike the Calculus of Variations, is rather di cult, we will deal with the intuition behind Optimal Control Theory instead.
We will make the following assump-tions, 1. uis unconstrained, so that the solution will always be in the interior. In other. AN OPTIMAL CAPITAL ACCUMULATION MODEL Consider a one-sector economy in which the stock of capital, denoted by K(t), is the only factor of production.
Let F(K) be the output rate of the economy when K is the capital stock. Assume F(0) = 0, F(K) > 0, F′(K) > 0, and F′′(K) latter implies the diminishing marginal productivity of capital.
Calculus of variations applied to optimal control: 7: Numerical solution in MATLAB: 8: Properties of optimal control solution. Bryson and Ho, Section and Kirk, Section 9: Constrained optimal control.
Bryson and Ho, section 3.x and Kirk, section Singular arcs. Optimal control theory of distributed parameter systems is a fundamental tool in applied mathematics.
Since the pioneer book by J.-L. Lions  published in many papers have been devoted to both its theoretical aspects and its practical applications. The present article belongs to the latter set: we review some work related. This course studies basic optimization and the principles of optimal control.
It considers deterministic and stochastic problems for both discrete and continuous systems. The course covers solution methods including numerical search algorithms, model predictive control, dynamic programming, variational calculus, and approaches based on Pontryagin's maximum principle, and it includes many.
This paper suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove new versions of the Pontryagin maximum principle.
Optimal Control Theory with Economic Applications by Seierstad and Sydsweter is intended as a rigorous treatment of the subject. Their book is the first in the economics literature to articulate the position of the eminent control theorist L. Young. Optimal Control Theory Version By Lawrence C.
Evans Department of Mathematics The next example is from Chapter 2 of the book Caste and Ecology in Social Insects, by G.
Oster and E. Wilson [O-W]. We attempt to model how social known rate at which each worker contributes to the bee economy. Part 2. THEORETICAL QUESTIONS OF OPTIMAL CONTROL THEORY Stabilization of Control Systems by Means of High-Gain Feedback H.W.
Knobloch Sequential Quadratic Programming and its Use in Optimal Control Model Comparisons n Investigation of Some Inventory Problems with Linear Replenishment Cost by the Method of Region Analysis. on adaptive management are rooted in parallel concepts found in business (total quality management and learning organizations ), experimental science (hypothesis testing ), systems theory (feedback control ), and industrial ecology (7).
The concept has attracted attention as a means of linking learning with policy and implementation (8,9). to optimal control theory Christiane P. Koch Laboratoire Aim´e Cotton CNRS, France The Hebrew University Jerusalem, Israel.
Outline 0. Terminology 1. Intuitive control schemes and their experimental realization 2. Controllability of a quantum system 3.
Variational approach to quantum control 4. Experimental quantum control: closed learning loops.Optimal Control Applications & Methods provides a forum for papers on the full range of optimal control and related control design methods. The aim is to encourage new developments in optimal control theory and design methodologies that may lead to advances in real control applications.
Read the journal's full aims and scope.Geared toward upper-level undergraduates, this text introduces three aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization.
Chapters 1 and 2 focus on describing systems and evaluating their performances. Chapter 3 deals with dynamic programming.