One of the most remarkable results in linear control theory and design is that if the cost criterion is quadratic, and the optimization is over an in. Our goal is to design a state feedback to stabilize a system under uncertainty. Once the optimal path or value of the control variables is found, the. Automatic control 2 optimal control and estimation. A hierarchical control architecture for balancing comfort and energy consumption in buildings is presented.
Robust optimal control with adjustable uncertainty sets. An optimal control approach to robust control of robot. Whereas in the adaptive control approach the learning dynamics is exterior to the control problem, in the dual control approach it is recognized that learning and control are interrelated and the optimal solution for combined learning and control problem is computed. Optimal control and estimation automatic control 2 optimal control and estimation prof. Robust control design rsp series in control theory and applications series editor.
Advanced topics with matlab offers a straightforward, selfcontained handbook of advanced topics and tools in automatic control. In the early time, robust control design was based on frequency domain. Robust sampleddatah2 and fault detection and isolation mike lind rank department of automation technical university of denmark ph. Because the uncertainty bound is reflected in the cost, the solution to the optimal control problem is a solution to the robust control problem. An introduction to optimal control applied to disease models. A general approach analytical solutions can be found even for system with more switching points when their number is known. In optimal control theory, after formulating a problem appropriate to the scenario, there are several basic problems. Here we obtain a more natural form of lqg duality by replacing the kalmanbucy. The results constitute, from several points of view, the current state of the art for standard optimal control problems. The main idea is the integration of optimal control and parameter estimation. The novel use of the twoport system in this context allows straightforward engineeringoriented.
It has numerous applications in both science and engineering. Because robust control requires a variety of skills to build accurate models of the system, it is related to the system approach of using multidisciplinary design teams. Use features like bookmarks, note taking and highlighting while reading optimal control and estimation dover books on mathematics. Robust control systems are especially concerned with the uncertainty included with the measurement of sensors. As such, the optimal state estimate is applied to design the optimal control law. An optimal control approach to robust controller design for the uncertain system has been reported in 1619. Theory and algorithms for indirect methods in optimal control. The main objective of this monograph is to present a broad range of well worked out, recent theoretical and application studies in the field of robust control system analysis and design. Alberto bemporad university of trento academic year 20102011 prof. These turn out to be sometimes subtle problems, as the following collection of examples illustrates. The optimal control problem we are interested in consists in nding the variable in time steam temperature minimizing the energy cost and maximizing the nutrient retention, while satisfying the constraint 1. Although the issue of mixed constraints is broached, it is not completely developed.
Robust and optimal control ebook by dawei gu 9781447162575. An engineering approach to optimal control and estimation theory is an invaluable, selfcontained reference for practicing engineers, a useful text for graduate students and qualified senior undergraduates, and an important resource for anyone interested in the future of modern control technology. Conclusions the optimal control approach allowed us to formulate problems of inventoryproduction control at considerable level of generality. Regarding the second point, we investigate a robust control design approach that. Robust control considers the design of decision or control rules that fare well across a range of alternative models.
This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. While there are many books on advanced control for specialists, there are few that present these topics for nonspecialists. Robust methods aim to achieve robust performance andor stability in the presence. An introduction to optimal control problem the use of pontryagin maximum principle j erome loh eac bcam 0607082014 erc numeriwaves course j. An introduction to mathematical optimal control theory. Brandt abstract we present a new optimal control approach to robust control of robot manipulators in the framework of lin et al 7. Robust control originated in the 1980s in the control theory branch of the engineering and. We propose an optimal control approach to robust control design. The design of robust control systems the design of robust control systems is based on two tasks. Our team brings together a multitude of experience and knowledge in building system management and applications. Optimal control systems management strategy is strictly handson, therefore. This design process is done with complete knowledge of the plant.
This task presents us with these mathematical issues. Some applications of optimal control theory of distributed. Pdf we propose a new approach to robust control of nonlinear systems. An alternative approach is a variational approach that directly nds the optimal.
Alberto bemporad university of trento automatic control 2 academic year 20102011 1 32. The company at present employs 50 permanent staff members, and also makes use of specialist suppliers as needed. A set of di erential equations are used with speci c control rates that minimize an objective functional, which include all the variables that will be minimized. The main idea is to combine the eventtriggering mechanism with adaptive critic designs, so as to. Comprehensive and accessible guide to the three main approaches to robust control design and its applications optimal control is a mathematical field that is. Theoretical results and algorithms for indirect methods in optimal control of hybrid sys. Dynamic modeling, model linearization, optimal control design, refrigerator system 1. An optimal control approach to robust control design. It was developed by inter alia a bunch of russian mathematicians among whom the. In particular, time dependence as well as inventory level dependence of demand is a feature which existing inventory models do not have. General duality between optimal control and estimation emanuel todorov abstract optimal control and estimation are dual in the lqg setting, as kalman discovered, however this duality has proven dif. Third, in contrast to most of the literature, we derive closedform robust ordering rate functions for a basic static.
Thus robust control is inherently about model uncertainty, particularly focusing on the implications of model uncertainty for decisions. Practical performance and design algorithms for industrial and aerospace systems f. Optimal control theory is a modern approach to the dynamic optimization without being constrained to interior solutions, nonetheless it still relies on di erentiability. An optimal control approach operations research, 2018, vol. To achieve an optimal solution to the robust control problem there is a need to minimize a cost functional. We translate this robust control problem into an optimal control problem of minimizing a cost. Mar 18, 2017 while there are many books on advanced control for specialists, there are few that present these topics for nonspecialists. Robust control encyclopedia of life support systems. Highlights a new approach for designing robust controller for fuzzy parametric uncertain systems fpus is proposed. In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Robust controller design for fuzzy parametric uncertain. Loh eac bcam an introduction to optimal control problem 0607082014 1 41. Introduction and basic elements of control systems 2. Robust control, theory and applications intechopen.
The control design is based on a simplified, yet accurate model of the temperature. Optimal control homework exercise 3 december 17, 2010 in this exercise two di erent problems will be considered, rst the so called zermelo problem where the problem is to steer a boat in streaming water, and then a problem where the thrust angle is controlled to obtain the maximum orbit radius of a space shuttle. In this work, a simplified modelbased optimal control model with adjustable parameters is constructed. However, optimal controllers can bevery sensitive to model errors. Assuming only a basic knowledge of automatic control and signals and systems, optimal and robust control. Solution methods for optimal control problems demo example with nlp local collocation implicit runge kutta. Ltr lqg offers a great way to design controllers for mimo systems to achieve some desired performance speci. The novel use of the twoport system in this context allows straightforward engineeringoriented solutionfinding procedures to be. Optimal control theory emanuel todorov university of california san diego optimal control theory is a mature mathematical discipline with numerous applications in both science and engineering. Result is optimal control sequence and optimal trajectory.
Robust methods aim to achieve robust performance andor stability in the presence of bounded modelling errors. These equations can be complicated, and exact solution of the hamiltonjacobi equations for nonlinear systems may not be possible. Robust control problem is solved via optimal control approach. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to. The book is largely selfcontained and incorporates numerous simplifications and.
Theory and algorithms for indirect methods in optimal. Pdf control, estimation and optimization of energy. For merging of links andor onramps in traffic networks, a merge node is. Chapter 2 optimal control optimal control is the standard method for solving dynamic optimization problems, when those problems are expressed in continuous time. Optimal control theory is a branch of applied mathematics that deals with finding a control law for a dynamical system over a period of time such that an objective function is optimized. The last chapter, on optimal adaptive control, gives practical methods for solving these matrix design equations. Applications of the small gain theorem to robust control. This paper proposes an optimal control approach for a robust control design problem of the neutral type timedelay systems, taking parameter uncertainties and state delay into account. Because of the unknown load placed on a manipulator and the other uncertainties in the manipulator dynamics, it is. Lqr control has been applied by appropriate objective function formulation followed by simulation and comparison with other control strategies. The structure of the controller is chosen such that. Optimal control and estimation linear quadratic regulation solution to lq optimal control problem the solution u 2 6 6 4 u 0 u 1 u n 1 3 7 7 5 h 1f.
Fpus are converted into interval system for each alpha cut. Pdf modelbased hierarchical optimal control design for. Graduatelevel text provides introduction to optimal control theory for stochastic systems, emphasizing application of basic concepts to real problems. An introduction to mathematical optimal control theory version 0.
Numerical examples and simulations demonstrate robustness of the proposed controller. The optimal control law is the one which minimizes the cost criterion. Optimal control and estimation dover books on mathematics kindle edition by stengel, robert f download it once and read it on your kindle device, pc, phones or tablets. It is emerging as the computational framework of choice for studying the neural control of movement, in much the same way that probabilistic infer. Optimal control is a powerful optimization technique used to derive the best control strategies. General duality between optimal control and estimation. Optimal control systems was formed in november 1993.
Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some typically compact set. Dynamic modeling, optimal control design and comparison. Kemin zhou, louisiana state university john doyle, california institute of technology keith glover, university of cambridge. Stochastic optimal control theory bert kappen snn radboud university nijmegen the netherlands july 5, 2008. Theoretical results and algorithms for indirect methods in optimal control of hybrid systems are introduced that overcome limitations and increase the competitiveness in comparison with direct methods and dynamic programming. An optimal control approach offers a complete presentation of this approach to robust control design, presenting modern control theory in an concise manner. From classical to quantum optimal, stochastic, and. Suppose we own, say, a factory whose output we can control. Optimal control in continuous space and time contains many complications related. Control, estimation and optimization of energy efficient buildings conference paper pdf available in proceedings of the american control conference 4. Pontryagins maximum principle validates the existence of an optimal control 11.
The applications include tracking problem in robot manipulator 2021, setpoint regulation in cstr system etc. Invaluable as a reference for those already familiar with the subject. An engineering approach to optimal control and estimation. Modeling the spread of ebola with seir and optimal control. Japanese translation 1997, cover chinese translation 2002 you can find exercise problems in the book essentials of robust control summary of the book click here essentails of robust control robust and optimal control publications. Theory and algorithms for indirect methods in optimal control of hybrid systems. It was developed by inter alia a bunch of russian mathematicians among whom the central character was pontryagin. Whereas in the adaptive control approach the learning dynamics is exterior to the control problem, in the dual control approach it. The novel use of the twoport system in this context allows straightforward engineeringoriented solutionfinding procedures. Pdf optimal control approach for robust control design. The approach di ers from calculus of variations in that it uses control variables to optimize the functional. The book is largely selfcontained and incorporates numerous simplifications and unifying features for the subjects. Lecture notes principles of optimal control aeronautics.
Io all real control systems require some form of io. In what follows we study, from a mathematical point of view, an optimal control problem including the one. A twoport framework for robust and optimal control introduces an alternative approach to robust and optimal controller synthesis procedures for linear, timeinvariant systems, based on the twoport system widespread in electrical engineering. The contributions presented here include but are not limited to robust pid, hinfinity, sliding mode, fault tolerant, fuzzy and qft based control systems. Optimal control theory and the linear bellman equation. A robust optimal control for a four wheel robot by the decomposition. Optimal control and estimation dover books on mathematics.
Optimal control theory and the linear bellman equation hilbert j. Optimal control relies on solving the matrix design equations developed in the book. The second approach is a novel indirect method for hybrid optimal control problems. Optimal control brings together many of the important advances in nonsmooth optimal control over the last several decades concerning necessary conditions, minimizer regularity, and global optimality conditions associated with the hamiltonjacobi equation. An optimal control approach to robust control of robot manipulators feng lin and robert d. Unfortunately, such problems are computationally intractable in general, since they subsume the standard robust optimal control problem with xed uncertainty set.