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. A numerical solution for fractional optimal control problems. The efficiency of the method has been demonstrated on numerical example and illustrated by graphs. Problem of time optimal control of linear systems with fractional caputo derivatives is examined using technique of attainability sets and their support functions. Pseudospectral methods for infinitehorizon nonlinear optimal. Special issue optimal control and nonlinear dynamics in. Mar 01, 2017 we have considered an optimal control problem governed by fractional order differential equations modeling an hivimmune system. One of the fractional discretization method has been presented in 20. In both cases the control function was proposed as a feedback control obtained via minimization of the appropriate cost function. We introduce a formulation for the time optimal control problems of systems displaying fractional dynamics in the sense of the riemannliouville fractional derivatives operator. 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.
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. 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. Formulation of eulerlagrange equations for multidelay. We present a necessary optimality conditions for a class of optimal control problems.
A new method for numerical computation of optimal dynamic programming problem has been presented. Consensus of fractionalorder heterogeneous multiagent systems. Optimal control of discretetime fractional multiagent. Improve your logic, think more critically, and use proven systems to solve your problems strategic planning for everyday life kindle edition. Fractional optimal control problems with specified final time. 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. Fractional order state equations for the control of. Optimal control of linear systems with fractional derivatives. The fractional derivative in the dynamic system is described in the caputo sense. A global optimization approach to fractional optimal control. 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.
We develop generalized eulerlagrange equations that results from multidelay fractional optimal control problems focp with final terminal. Get a printable copy pdf file of the complete article 584k, or click on a page image below to browse page by page. 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. Sep 23, 2014 tracking and other problems of linear quadratic optimal control are discussed in chapter 4. The numerical simulation of the fractional order control systems has been investigated in 7. Due to concerns over commercial postings on the system dynamics main topic, commercial hyperlinks are specifically not active on this list. 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.
So far the optimal control of continuoustime systems is described. A linear system of fractional differential equations. 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. It describes the development of modelbased control design methods for systems described by fractional dynamic models. An approximate method for numerically solving fractional. This paper presents a general formulation and solution scheme of a class of fractional optimal control problems.
Fractional variational integration and optimal control. An introduction to mathematical optimal control theory version 0. Dynamical analysis of chemotherapy optimal control using. An analytic solution of the time optimal problem is proposed, and the optimal transfer route is provided. An important class of continuoustime optimal control problems are the socalled linearquadratic optimal control problems where the objective functional j in 3. Optimal control problem for fractional dynamic systems. Full text full text is available as a scanned copy of the original print version. 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.
Sufficient conditions for time optimal control similar to that of pontryagins maximum principle are obtained for. Pdf on timeoptimal control of fractionalorder systems. Extension of the wienerhopf design method to the case of fractional order processes with time delay. We also discuss the gain and phase margins of the lqr system. Nov 23, 2015 this paper deals with the time optimal control problem for a class of fractional order systems. 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. This is a comparison of various aspects of software offering system dynamics features.
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 problem is a hard nonconvex optimal control problem and application of pontriyagins principle does not always guarantee finding a global optimal control. 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. In this paper, an efficient linear programming formulation is proposed for a class of fractional order optimal control problems with delay argument. An approximate method for numerically solving fractional order optimal control problems of general form. Fractionalorder modeling and control of dynamic systems. The rational for using fractional differential equations is to account for the fact that the immune response involves memory.
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. Fractional kalman filter and its application have been addressed in 25, 26. 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. Nonlinear dynamics, bifurcations, and chaos in electrical power systems.
Dynamic programming problem for fractional discrete time systems with quadratic performance index has been formulated and solved. 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. 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. Oct 28, 2010 a constrained dynamic optimization problem of a fractional order system with fixed final time has been considered here. 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. 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.
Even this type of problems in a finite dimensional space is known as np hard. Fractional optimal control problems with several state and. The dynamical control system involves integer and fractional order derivatives and the final time is free. Evans department of mathematics university of california, berkeley. It also treats both continuous time and discrete time optimal control systems, giving students a firm grasp on both methods. 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.
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. Many different foc schemes are presented for control and dynamic systems problems. The fractional optimal control has been recently addressed in some recent works. Fractional optimal control problem is treated from convexanalytical viewpoint. Topics of interest include, but are not limited to. Optimal control systems electrical engineering series. Problem of time optimal control of linear systems with fractional dynamics is treated in the paper from the convexanalytic standpoint. Supports system dynamics, monte carlo simulation for uncertainty, array abstraction for handling multidimensional data. This optimal control problem can, in principle, be solved by dinkhelbach algorithm 10. Optimal control of dynamic systems stanford online. Students will learn to use different mathematical models, performance indexes, variables and boundaries that are used to understand the foundations of optimal.
New results on the application of control of a laboratory hydraulic canal prototype that has fractional order dynamics. Timeoptimal control of systems with fractional dynamics. Time fractional optimal control problems using the. Some optimal control problems for fractional order systems have been investigated in 15, 11, 12, 27. Electromechanical systems appear in many areas of the automotive industry with optimal control problems arise in areas such as hybrid powertrain control. Pdf timeoptimal control of linear fractional systems. Fractional calculus, delay dynamics and networked control systems. 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.
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. Specifically, time optimal bangbang controls will be investigated. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations. Timeoptimal control of fractional dynamic systems request pdf. Feedback control laws for linear dynamic system are obtained. Dynamic programming for fractional discretetime systems. Suboptimal control of fractionalorder dynamic systems with. 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. Dynamics feature and synchronization of a robust fractional. This book reports on an outstanding research devoted to modeling and control of dynamic systems using fractional order calculus. On the fractional optimal control problem with free end. This paper presents a new numerical method for solving fractional optimal control problems focps. Once workable theory and software has been developed, they will be evaluated in two automotive projects.
551 1364 861 301 1290 1112 1122 124 117 180 154 472 910 979 1279 495 562 32 1259 1351 324 1192 1027 1156 1081 920 1096 998 1082 665 805