Timeoptimal control of fractional dynamic systems conference paper in proceedings of the ieee conference on decision and control january 2010 with 54 reads how we measure reads. A global optimization approach to fractional optimal control. Sufficient conditions for time optimal control similar to that of pontryagins maximum principle are obtained for. Optimal control systems electrical engineering series. Fractional calculus, delay dynamics and networked control systems. Feedback control laws for linear dynamic system are obtained. Fractional optimal control problems with several state and. An analytic solution of the time optimal problem is proposed, and the optimal transfer route is provided. Fractional order systems timeoptimal control and its. Optimal control problem for fractional dynamic systems. To propose a solution to the general time optimal problem, a rational approximation based on the hankel data matrix of the impulse response is considered to emulate the. A method to construct a control function that brings trajectory of the system to a strictly convex terminal set in the shortest time is elaborated.
Even this type of problems in a finite dimensional space is known as np hard. New results on the application of control of a laboratory hydraulic canal prototype that has fractional order dynamics. Time optimal control of fractional dynamic systems conference paper in proceedings of the ieee conference on decision and control january 2010 with 54 reads how we measure reads. The rational for using fractional differential equations is to account for the fact that the immune response involves memory. Sufficient conditions for time optimal control similar to that of pontryagins maximum principle are obtained for fractional order systems in the sense of riemannliouville and caputo. Topics of interest include, but are not limited to. Many different foc schemes are presented for control and dynamic systems problems. The fractional derivative in the dynamic system is described in the caputo sense. Extension of the wienerhopf design method to the case of fractional order processes with time delay. Fractional order state equations for the control of. Nov 23, 2015 this paper deals with the time optimal control problem for a class of fractional order systems. As the examples to explain our analysis, we select two sets of coupling parameters k 2 1, k 3 4 and k 2 10, k 3 4 to realize the optimal synchronization.
Control theory in control systems engineering is a subfield of mathematics that deals with the control of continuously operating dynamical systems in engineered processes and machines. Optimal control of dynamic systems stanford online. Fractional variational integration and optimal control. Full text full text is available as a scanned copy of the original print version. Fractionalorder modeling and control of dynamic systems. Students will learn to use different mathematical models, performance indexes, variables and boundaries that are used to understand the foundations of optimal. Supports system dynamics, monte carlo simulation for uncertainty, array abstraction for handling multidimensional data. Nonlinear dynamics, bifurcations, and chaos in electrical power systems. Optimal control of discretetime fractional multiagent.
Led by omar sheikh, the team is compose of a diverse group of majors whose focus is to create software suite for academics and industrial applications. This paper presents a new numerical method for solving fractional optimal control problems focps. So far the optimal control of continuoustime systems is described. Timeoptimal control of systems with fractional dynamics christophe tricaud and yangquan chen center for selforganizing and intelligent systems csois, department of electrical and computer engineering, utah state university, 41260 old main hill, logan, ut 843224160, usa. If there are no path constraints on the states or the control variables, and if the initial and final times are fixed, a fairly general continuous time optimal control problem can be defined as follows. Among this books most outstanding features is a summary table that accompanies each topic or problem and includes a statement of the problem with a stepbystep solution. Variable structure control of linear time invariant fractional order systems using a finite number of state feedback law communications in nonlinear science and numerical simulation, vol. Timeoptimal control of fractional dynamic systems request pdf.
Apr 06, 2012 continuous time optimal control using the variational approach general case with fixed final time and no terminal or path constraints. Wienerhopf optimal control of a hydraulic canal prototype. We introduce a formulation for the time optimal control problems of systems displaying fractional dynamics in the sense of the riemannliouville fractional derivatives operator. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems.
This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional order calculus. Problem of time optimal control of linear systems with fractional dynamics is treated in the paper from the convexanalytic standpoint. We develop generalized eulerlagrange equations that results from multidelay fractional optimal control problems focp with final terminal. Suboptimal control of fractionalorder dynamic systems with. This is a comparison of various aspects of software offering system dynamics features. It also treats both continuous time and discrete time optimal control systems, giving students a firm grasp on both methods. Timeoptimal control of systems with fractional dynamics. The efficiency of the method has been demonstrated on numerical example and illustrated by graphs. The dynamical control system involves integer and fractional order derivatives and the final time is free. We also discuss the gain and phase margins of the lqr system. Electromechanical systems appear in many areas of the automotive industry with optimal control problems arise in areas such as hybrid powertrain control. One of the fractional discretization method has been presented in 20. In this paper, an efficient linear programming formulation is proposed for a class of fractional order optimal control problems with delay argument.
Next, the optimal control of discretetime systems is presented in chapter 5. May 23, 2012 a real time algorithm for nonlinear infinite horizon optimal control by time axis transformation method 9 july 2012 international journal of robust and nonlinear control, vol. A new method for numerical computation of optimal dynamic programming problem has been presented. Evans department of mathematics university of california, berkeley. Some optimal control problems for fractional order systems have been investigated in 15, 11, 12, 27. In this paper, we addressed the problem of control strategies for two types of discrete time fractional multiagent systems, with single and double summator dynamics. It is largely selfcontained, covering the fundamentals of fractional calculus together with some analytical and numerical techniques and providing matlab codes for the simulation of fractionalorder control foc systems. Considering it is usually adopted in the discrete situation for actual control system, the sampling date may induce chattering phenomenon, an alternative sub optimal solution is constructed. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations. Problem of time optimal control of linear systems with fractional caputo derivatives is examined using technique of attainability sets and their support functions.
Dynamic programming for fractional discretetime systems. Due to concerns over commercial postings on the system dynamics main topic, commercial hyperlinks are specifically not active on this list. Fractional dynamics and control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. Sep 23, 2014 tracking and other problems of linear quadratic optimal control are discussed in chapter 4. Improve your logic, think more critically, and use proven systems to solve your problems strategic planning for everyday life kindle edition. An approximate method for numerically solving fractional order optimal control problems of general form. In this paper, we develop a computational approach to motor control that offers a unifying modeling framework for both dynamic systems and optimal control approaches. The fractional optimal control has been recently addressed in some recent works. A numerical solution for fractional optimal control problems. In both cases the control function was proposed as a feedback control obtained via minimization of the appropriate cost function. The numerical simulation of the fractional order control systems has been investigated in 7. Consensus of fractionalorder heterogeneous multiagent systems. Formulation of eulerlagrange equations for multidelay. Time fractional optimal control problems using the.
Dynamical analysis of chemotherapy optimal control using mathematical model presented by fractional differential equations, describing effector immune and cancer cells interactions mehdi shahbazi 1, g hussian erjaee 1, and hoda erjaee 2. Mar 01, 2017 we have considered an optimal control problem governed by fractional order differential equations modeling an hivimmune system. It can be found that we can realize the partial phase synchronization of fractional chaotic system with the selected coupling parameters, but larger parameters k 2 and k 3 will lead to shorter synchronous transition time, as. It describes the development of modelbased control design methods for systems described by fractional dynamic models. We present a necessary optimality conditions for a class of optimal control problems. An important class of continuoustime optimal control problems are the socalled linearquadratic optimal control problems where the objective functional j in 3. The objective is to develop a control model for controlling such systems using a control action in an optimum manner without delay or overshoot and ensuring.
Special issue optimal control and nonlinear dynamics in. Oct 28, 2010 a constrained dynamic optimization problem of a fractional order system with fixed final time has been considered here. Pdf timeoptimal control of linear fractional systems. Dynamics feature and synchronization of a robust fractional. Time optimal control of systems with fractional dynamics christophe tricaud and yangquan chen center for selforganizing and intelligent systems csois, department of electrical and computer engineering, utah state university, 41260 old main hill, logan, ut 843224160, usa. An approximate method for numerically solving fractional. Fractional kalman filter and its application have been addressed in 25, 26.
Fractional optimal control problem is treated from convexanalytical viewpoint. This optimal control problem can, in principle, be solved by dinkhelbach algorithm 10. Dynamic programming problem for fractional discrete time systems with quadratic performance index has been formulated and solved. Energies is pleased to invite prospective authors to submit original research submissions covering innovations associated with the use of optimal control and nonlinear dynamics in electrical power systems. To propose a solution to the general time optimal problem, a rational approximation based on the hankel data matrix of the impulse response is considered to emulate the behavior of the fractional differentiation. Fractional optimal control problems with specified final time.
Dynamical analysis of chemotherapy optimal control using. In this paper, a new numerical scheme is proposed for multidelay fractional order optimal control problems where its derivative is considered in the grunwaldletnikov sense. Optimal control of linear systems with fractional derivatives. Get a printable copy pdf file of the complete article 584k, or click on a page image below to browse page by page. This study is devoted to the consensus protocols design for a set of fractionalorder heterogeneous agents, which is composed of two kinds of agents differed by their dynamics and the fractionalorder. Pseudospectral methods for infinitehorizon nonlinear optimal.
A linear system of fractional differential equations. An introduction to mathematical optimal control theory version 0. Specifically, time optimal bangbang controls will be investigated. Pdf on timeoptimal control of fractionalorder systems. On the fractional optimal control problem with free end.
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