Result is optimal control sequence and optimal trajectory. 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. A twoport framework approach advances in industrial control. Bertsekas massachusetts institute of technology chapter 6 approximate dynamic programming this is an updated version of the researchoriented chapter 6 on approximate dynamic programming.
Once the optimal path or value of the control variables is found, the. Due to the unknown load placed on a manipulator and the other uncertainties in the manipulator dynamics, it is important to design a robust control law that will guarantee the performance of the manipulator under these uncertainties. An optimal control approach operations research, 2018, vol. Plot of the performance robust optimal control signal. Modeling,simulation and optimal control for an aircraft of. Robust control systems are especially concerned with the uncertainty included with the measurement of sensors. While there are many books on advanced control for specialists, there are few that present these topics for nonspecialists. The novel use of the twoport system in this context allows straightforward engineeringoriented. Optimal control approach for robust control design of uncertain time. Attention was then paid to the design of the control system by utilizing the lqr state feedback method and selftuning fuzzy control algorithm. An optimal control approach to robust control design taylor. Robust control design rsp series in control theory and applications series editor.
Highlights a new approach for designing robust controller for fuzzy parametric uncertain systems fpus is proposed. Pdf optimal control approach for robust control design. The main idea is the integration of optimal control and parameter estimation. Robust controller design for fuzzy parametric uncertain. 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. The last chapter, on optimal adaptive control, gives practical methods for solving these matrix design equations. A course in robust control theory a convex approach. Although the issue of mixed constraints is broached, it is not completely developed. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to. Optimal control theory is a systematic approach to controller design whereby the desired performance objectives are encoded in a cost function, which is subsequently optimized to determine the desired controller. 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. Our goal is to design a state feedback to stabilize a system under uncertainty. Because the uncertainty bound is reflected in the cost, the solution to the. This paper proposes an optimal control approach for the robust control design problem of the linear timedelay systems, which takes parameter uncertainties.
Trajectory optimization flight control trajectory optimization. A mean value theorem approach to robust control design. Pdf an optimal control based aproach to dynamics autonomous. The modern control approach is to break the problem into two pieces. Use features like bookmarks, note taking and highlighting while reading optimal control and estimation dover books on mathematics. A chapter on optimal control of polynomial systems is designed to give the reader sufficient background for further study in the field of adaptive control. Dynamic programming and optimal control 3rd edition, volume ii. A mean value theorem approach to robust control design for uncertain nonlinear systems obaid ur rehman ian r. 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. Optimal control and maximum principle daniel wachsmuth, ricam linz ems school bedlewo bedlewo, 12. 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.
The optimal control law is the one which minimizes the cost criterion. A computational approach is developed for designing a globally optimal controller which is robust to timevarying nonlinear perturbations in the plant. An optimal control approach offers a complete presentation of this approach to robust control design, presenting modern control theory in an concise manner. 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. Whereas in the adaptive control approach the learning dynamics is exterior to the control problem, in the dual control approach it. This research activity has been at the confluence of dynamical systems theory, functional analysis, matrix analysis, numerical methods, complexity theory. We propose an optimal control approach to robust control design. For this reason the approach is said predictive, as in fact the optimal control problem is formulated over a timeinterval that starts at the current time up to a certain time in the future. Murray optimal control 7 february 2007 this lecture provides an overview of optimal control theory. Practitioners will also find the applications presented useful when solving practical problems. The main result of this period was the wienerkolmogorov theory that addresses linear siso systems with gaussian noise. The book is largely selfcontained and incorporates numerous simplifications and. A survey of numerical methods for trajectory optimization. Lqr control has been applied by appropriate objective function formulation followed by simulation and comparison with other control strategies.
Robust optimal control with adjustable uncertainty sets. This controller design problem is formulated as an optimization with bilinear matrix inequality bmi constraints, and is solved to optimality by a branch and bound algorithm. While the nonadaptive version the setpoint control problem is very well understood and has been so for more than. Robust sampleddatah2 and fault detection and isolation mike lind rank department of automation technical university of denmark ph. It can also handle uncertainty in the control input matrix. Bhattacharyya encyclopedia of life support systems eolss summary robust control is that branch of control theory which deals explicitly with system uncertainty and how it affects the analysis and design of control systems.
An engineering approach to optimal control and estimation. Robust control encyclopedia of life support systems. Hybrid control systems are mathematical models of heterogeneous. The approach di ers from calculus of variations in that it uses control variables to optimize the functional. Optimal control theory is a modern approach to the dynamic optimization without being constrained to interior solutions, nonetheless it still relies on di erentiability. Pdf an optimal control approach to robust control of. General duality between optimal control and estimation. The novel use of the twoport system in this context allows straightforward engineeringoriented solutionfinding procedures. The result of the optimization is an optimal sequence of future control moves.
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. Numerical examples and simulations demonstrate robustness of the proposed controller. Kemin zhou, louisiana state university john doyle, california institute of technology keith glover, university of cambridge. Shuttle reentry the problem is to control the reentry of the shuttle, from orbit to landing. 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. Because of the unknown load placed on a manipulator and the other uncertainties in the manipulator dynamics, it is important to design a robust control law that. Robust optimal control of linear discretetime systems. From this feedback loop, student will design the controllers with different strategies as the main objective of the laboratory practice, for example. Citeseerx document details isaac councill, lee giles, pradeep teregowda. The optimal control problem may be interpreted as an extension of the nonlinear programming problem to an in. Robust and optimal control of uncertain dynamical systems.
State variable approach, the state regulator problem, the infinitetime regulator problem, the output regulator and the tracking problems, parameter optimization. Currently the optimal hybrid control systems have become a new approach to nonlinear control theory see e. 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. Because the uncertainty bound is reflected in the cost, the solution to the optimal control problem is a solution to the robust control problem. It has numerous applications in both science and engineering. In this work, a simplified modelbased optimal control model with adjustable parameters is constructed. Optimal control theory and the linear bellman equation hilbert j. Com parisons are made between the robust optimal solution and a nonrobust nominal optimal solution.
An introduction to optimal control applied to disease models. We translate this robust control problem into an optimal control problem of minimizing a cost. Optimal control relies on solving the matrix design equations developed in the book. Based on the block diagram we get gc s y s r s g s f s 1 g s f s then solving for f s yields f s 1 g s y s r s 1 y s r s 1 from this it can be observed that if perfect control is desired, i. Essentials of robust control division of electrical. It is emerging as the computational framework of choice for studying the neural control of movement, in much the same way that probabilistic infer. Download it once and read it on your kindle device, pc, phones or tablets. 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. Fpus are converted into interval system for each alpha cut. Assuming only a basic knowledge of automatic control and signals and systems, optimal and robust control. Third, in contrast to most of the literature, we derive closedform robust ordering rate functions for a basic static. Relations to classical control theory are emphasized throughout the text, and a rootlocus approach to steadystate controller design is included.
Pdf optimal robust controller design for the ball and plate. An optimal control approach will be of interest to those needing an introductory textbook on robust control theory, design and applications as well as graduate and postgraduate students involved in systems and control research. Unfortunately, such problems are computationally intractable in general, since they subsume the standard robust optimal control problem with xed uncertainty set. An optimal control approach to robust control design. Theory and algorithms for indirect methods in optimal control. While the nonadaptive version the setpoint control problem is very well understood and has been so for more than a half century, the adaptive version still is not because there. Optimal control and estimation dover books on mathematics. We say that a controller is robust if it works even if the actual system deviates from. An optimal control approach to robust control design 1997. Dynamic programming and optimal control 3rd edition, volume ii by dimitri p. This current investigation firstly focused on establishing the lateral nonlinear model and the lateral control strategy.
Optimal control is a mathematical field that is concerned with control policies that can. 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. In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. In particular, time dependence as well as inventory level dependence of demand is a feature which existing inventory models do not have. For fundamental background in the associated calculusofvariations the readershouldreferto bliss. 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. A twoport framework for robust and optimal control features. We present a new optimal control approach to robust control of robot manipulators in the framework of lin 1997. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some typically compact set. Robust and optimal control ebook by dawei gu 9781447162575.
Io all real control systems require some form of io. The results constitute, from several points of view, the current state of the art for standard optimal control problems. The novel use of the twoport system in this context allows straightforward engineeringoriented solutionfinding procedures to be. As such, the optimal state estimate is applied to design the optimal control law.
Dynamic modeling, optimal control design and comparison. Graduatelevel text provides introduction to optimal contro. An optimal control approach to robust control design is proposed in this study for rigid robotic systems under the unknown load and the other uncertainties. Use features like bookmarks, note taking and highlighting while reading robust and optimal control. Dynamic modeling, model linearization, optimal control design, refrigerator system 1. Optimal control theory and the linear bellman equation. I optimal control is an approach to control systems design that seeks the best possible control with respect to a performance metric. Robust methods aim to achieve robust performance andor stability in the presence of bounded modelling errors. A twoport framework approach advances in industrial control kindle edition by tsai, miching, gu, dawei. 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.
Conclusions the optimal control approach allowed us to formulate problems of inventoryproduction control at considerable level of generality. The focus of the third part is the application of the previously introduced methods and procedures to the design of robust and optimal control strategies for dynamical systems with statedependent switching characteristics 8. For example, the dynamical system might be a spacecraft with controls corresponding to rocket. 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. Pdf we present a new optimal control approach to robust control of. I the theory of optimal control began to develop in the ww ii years. Pdf this paper proposes an optimal control approach for a robust control design problem of the neutral type timedelay systems, taking. However, optimal controllers can bevery sensitive to model errors. An optimal control approach to robust control design semantic. The book is largely selfcontained and incorporates numerous simplifications and unifying features for the subjects. Pdf optimal control approach for robust control design of neutral. An excellent introduction to optimal control and estimation theory and its relationship with lqg design. Robust control problem is solved via optimal control approach. An optimal control approach to robust control of robot.
These equations can be complicated, and exact solution of the hamiltonjacobi equations for nonlinear systems may not be possible. Feng lin comprehensive and accessible guide to the three main approaches to robust control design and its applications. Pdf an optimal control approach to robust control of robot. Dynamic programming and optimal control 3rd edition. In optimal control theory, after formulating a problem appropriate to the scenario, there are several basic problems.