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1.
A new approach to the problem of optimal control of linear dynamic systems is proposed that makes use of a method of input and state parametrization to transform the original problem into a problem of the Calculus of Variations. In contrast to the standard approaches for this class of problems, two salient features of the new approach are that no Lagrange multiplier functions need to be invoked and that the class of inputs can be restricted to the - relatively small - class of continuous functions, even for problems with fixed end-states. The resulting necessary conditions of optimality, i.e., the Euler-Lagrange equation and the boundary conditions for the transformed problem, are proved to be equivalent to those resulting from the standard method of First Variations. In case of quadratic cost functionals, the new approach provides a simpler alternative to the well known, but equally difficult, Riccati differential equation approach and results in a simple dynamic state-feedback implementation of the optimal control.  相似文献   

2.
《Journal of The Franklin Institute》2023,360(14):10433-10456
An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach.  相似文献   

3.
In this paper, we consider the H2-optimal control problem subject to the constraint that the resulting controller be strictly positive real. A direct numerical optimization approach is adopted in conjunction with a controller parametrization that is linear in the unknown parameters. The SPR constraint is easily expressed at each frequency in the form of a linear inequality. The method is applied to a numerical example from the literature and good results are achieved. In particular, the proposed method is particularly adept at determining low order controllers.  相似文献   

4.
A recent communication has proposed a conjectural procedure for representing a category of optimal control problems in bond graph language [W. Marquis-Favre, B. Chereji, D. Thomasset, S. Scavarda, Bond graph representation of an optimal control problem: the dc motor example, in: ICBGM’05 International Conference of Bond Graph Modelling and Simulation, New Orleans, USA, January 23-27, 2005, pp. 239-244]. This paper aims at providing a fundamental theory for proving the effectiveness of this procedure. The class of problem that the procedure can deal with has been extended. Its application was formerly restricted to linear time invariant siso system. The systems considered now are linear time invariant mimo systems. The optimization objective is the minimization of dissipation and input. The developments concerning the optimal control problem are based on the Pontryagin maximum principle and the proof of the effectiveness of the procedure makes a broad use of the port-Hamiltonian concept. As a result, the bond graph representation of the given optimization problem enables the analytical system, which provides the optimal solution, to be derived. The work presented in this paper is the first step in research with perspectives towards formulating dynamic optimization problems in bond graph and, towards coupling this formulation with a sizing methodology using bond graph language and a state-space inverse model approach. This sizing methodology, however, is not the topic of this paper and thus is not presented here.  相似文献   

5.
The attitude tracking control problem for a rigid spacecraft using two optimal sliding mode control laws is addressed. Integral sliding mode (ISM) control is applied to combine the first-order sliding mode with optimal control and is applied to quaternion-based spacecraft attitude tracking maneuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the control Lyapunov function (CLF) approach is used to solve the infinite-time nonlinear optimal control problem, whereas the Lyapunov optimizing control (LOC) method is applied to solve the finite-time nonlinear optimal control problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking maneuvres is presented and simulation results are included to demonstrate and verify the usefulness of the proposed controllers.  相似文献   

6.
In precision motion systems, well-designed feedforward control can effectively compensate for the reference-induced error. This paper aims to develop a novel data-driven iterative feedforward control approach for precision motion systems that execute varying reference tasks. The feedforward controller is parameterized with the rational basis functions, and the optimal parameters are sought to be solved through minimizing the tracking error. The key difficulty associated with the rational parametrization lies in the non-convexity of the parameter optimization problem. Hence, a new iterative parameter optimization algorithm is proposed such that the controller parameters can be optimally solved based on measured data only in each task irrespective of reference variations. Two simulation cases are presented to illustrate the enhanced performance of the proposed approach for varying tasks compared to pre-existing results.  相似文献   

7.
An adaptive numerical method for solving multi-delay optimal control problems with piecewise constant delay functions is introduced. The proposed method is based on composite pseudospectral method using the well-known Legendre–Gauss–Lobatto points. In this approach, the main problem converts to a mathematical optimization problem whose solution is much more easier than the original one. The necessary conditions of optimality associated to nonlinear piecewise constant delay systems are derived. The method is easy to implement and provides very accurate results.  相似文献   

8.
A problem of stabilization about uncertain networked control systems (NCSs) with random but bounded delays is discussed in this paper. By using augmented state-space method, this class of problems can be modeled as discrete-time jump linear systems governed by finite-state Markov chains. A new switched model based on probability is proposed to research problems of reliable control when actuators become ageing or partially disabled. Using improved V-K iteration algorithm, a class of reliable controllers are designed to make systems asymptotically mean square stable under several stochastic disturbances such as random time-delay and stochastic actuator failure and the maximal redundancy degree is given through this method.  相似文献   

9.
In this paper, the quadratic minimax optimal control of linear system with input-dependent uncertainty is studied. We show that it admits a unique solution and can be approximated by a sequence of finite-dimensional minimax optimal parameter selection problems. These finite-dimensional minimax optimal parameter selection problems are further reduced to scalar optimization problems which also admit unique solutions. Thus, the original minimax optimal control problem is solved via solving a sequence of simple scalar optimization problems. Numerical experiments are presented to illustrate the developed method.  相似文献   

10.
Design of an optimal controller requires optimization of multiple performance measures that are often noncommensurable and competing with each other. Design of such a controller is indeed a multi-objective optimization problem. Non-dominated sorting in genetic algorithms-II (NSGA-II) is a popular non-domination based genetic algorithm for solving multi-objective optimization problems. This paper investigates the application of NSGA-II technique for the design of a flexible AC transmission system (FACTS)-based controller. The design objective is to improve the stability of the power system with minimum control effort. The proposed technique is applied to generate Pareto set of global optimal solutions to the given multi-objective optimization problem. Further, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto solution set. Further, a detailed analysis on the selection of control signals (both local and remote signals) on the effectiveness of the proposed controller is carried out and simulation results are presented under various loading conditions and disturbances to show the effectiveness and robustness of the proposed approach.  相似文献   

11.
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12.
This paper develops a new dual ML-ADHDP method to solve the optimal consensus problem (OCP) of a class of heterogeneous discrete-time nonlinear multi-agent systems (MASs) with unknown dynamics and time delay. A hierarchical and distributed control strategy is used to transform the original problem into nonlinear model reference adaptive control (MRAC) problems and an OCP of virtual linear MASs. For the nonlinear MRAC problems, a new multi-layer action-dependent heuristic dynamic programming (ML-ADHDP) method is developed to overcome the unknown dynamics and neural network estimation errors, which has higher control accuracy. In order to solve the OCP of virtual linear MASs and improve the convergence speed, a new multi-layer performance index is proposed. Then the ML-ADHDP method is used to solve the coupled Hamiltonian–Jacobi–Bellman equation and obtain the optimal virtual control. Theoretical analysis proves that the original MASs can achieve Nash equilibrium, and simulation results show that the developed dual ML-ADHDP method ensures better convergence speed and higher control accuracy of original MASs.  相似文献   

13.
This paper introduces an efficient direct approach for solving delay fractional optimal control problems. The concepts of the fractional integral and the fractional derivative are considered in the Riemann–Liouville sense and the Caputo sense, respectively. The suggested framework is based on a hybrid of block-pulse functions and orthonormal Taylor polynomials. The convergence of the proposed hybrid functions with respect to the L2-norm is demonstrated. The operational matrix of fractional integration associated with the hybrid functions is constructed by using the Laplace transform method. The problem under consideration is transformed into a mathematical programming one. The method of Lagrange multipliers is then implemented for solving the resulting optimization problem. The performance and computational efficiency of the developed numerical scheme are assessed through various types of delay fractional optimal control problems. Our numerical findings are compared with either exact solutions or the existing results in the literature.  相似文献   

14.
In this paper, a convex optimization algorithm is proposed to solve the online trajectory optimization problem of boost back of vertical take-off/vertical landing reusable launch vehicles. To achieve high-precision landing of launch vehicles, trajectory optimization of the boost-back flight phase considering the accuracy of entry is carried out, especially in emergencies. The trajectory optimization problem is formulated as an optimal control problem with minimum fuel consumption, and then it is transformed into a series of convex optimization subproblems, which can be solved by primal-dual interior-point method accurately and rapidly. During the transformation, flip-Radau pseudospectral discretization method, lossless convexification and successive convexification technology are applied. To drive the vehicle to predetermined entry points at the expected velocity, terminal constraints are expressed as orbital constraints of the endpoint in the boost-back flight phase. Considering the influence of Earth's rotation, the right ascension of the ascending node of the target orbit is updated according to the time and true anomaly at the end of the boost-back flight phase. Furthermore, the homotopy method is applied to the situation where there is no good initial guess when emergency happens. The algorithm presented in this paper performs well upon the simulation experiments of mission change and thrust decline. With good accuracy, high computational efficiency, and excellent robustness, the convex approach proposed has a great potential for onboard application in reusable launch vehicles and other space vehicles.  相似文献   

15.
In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.  相似文献   

16.
This paper is devoted to a theoretic framework for a general optimal control problem (OCP) associated with the classic sliding mode process. The sliding dynamic behavior is interpreted here as a special kind of additional constraints related to the main optimization problem. We are specially interested in the development of some adequate constructive approximations of the original OCPs. The mathematical approach based on the set-valued analysis allows to study the discontinuity of sliding mode dynamics in the abstract setting. Moreover, we also establish some sensitivity properties of the optimal solutions. The obtained results provide an universal analytical tool for the corresponding conceptual approximation schemes related to the original OCPs. The constructive approximations proposed in this paper are numerically stable and can be applied to various classes of optimal control processes governed by the affine control systems.  相似文献   

17.
利用变分法导出量子力学系统中一类最优控制问题的方程组，并使用具有最优搜索步长的开关变尺度法对最优控制问题进行数值迭代求解，最后在自旋1/2粒子上进行了系统仿真实验，验证了本文方法的有效性，同时对性能指标中参数的不同选择对整个最优控制效果影响的一般规律进行了分析。  相似文献   

18.
The vector space model (VSM) is a textual representation method that is widely used in documents classification. However, it remains to be a space-challenging problem. One attempt to alleviate the space problem is by using dimensionality reduction techniques, however, such techniques have deficiencies such as losing some important information. In this paper, we propose a novel text classification method that neither uses VSM nor dimensionality reduction techniques. The proposed method is a space efficient method that utilizes the first order Markov model for hierarchical Arabic text classification. For each category and sub-category, a Markov chain model is prepared based on the neighboring characters sequences. The prepared models are then used for scoring documents for classification purposes. For evaluation, we used a hierarchical Arabic text data collection that contains 11,191 documents that belong to eight topics distributed into 3-levels. The experimental results show that the Markov chains based method significantly outperforms the baseline system that employs the latent semantic indexing (LSI) method. That is, the proposed method enhances the F1-measure by 3.47%. The novelty of this work lies on the idea of decomposing words into sequences of characters, which found to be a promising approach in terms of space and accuracy. Based on our best knowledge, this is the first attempt to conduct research for hierarchical Arabic text classification with such relatively large data collection.  相似文献   

19.
In this paper, an integrated design of data-driven fault-tolerant tracking control is addressed relying on the Markov parameters sequence identification and adaptive dynamic programming techniques. For the unknown model systems, the sequence of Markov parameters together with the covariance of innovation signal is firstly estimated by least square method. After a transformation of value function from stochastic to deterministic, a policy iteration adaptive dynamic programming algorithm is then formulated to find the optimal tracking control law. In order to eliminate the influence of unpredicted faults, an active fault-tolerant supervisory control strategy is further constructed by synthesizing fault detection, isolation, estimation and compensation. All these involved designs are performed in the data-driven manner, and thus avoid the information requirement about system drift dynamics. From the perspective of system operation management, the above integrated control scheme provides a framework to achieve the tracking performance optimization, monitoring and maintaining simultaneously. The effectiveness of these conclusions is finally verified via two case studies.  相似文献   

20.
《Journal of The Franklin Institute》2022,359(18):11135-11154
A class of resource allocation problems with equality constraint are considered in this paper, such as economic dispatch problem in smart grid systems, which is essentially an optimization problem. Inspired by the Lagrange multiplier method, the resource allocation problem is transformed into a multi-agent consensus problem for large-scale networked distributed nodes. A consensus-based distributed fixed-time optimization algorithm is presented, where the information exchange network is depicted by a strongly connected and weight-balanced digraph. This type of communication network can ensure that the equality constraint always holds. Moreover, a new globally fixed-time stability theorem for nonlinear systems is first given in this paper. Based on this theorem and consensus theory, the optimal resource allocation scheme can be given in a fixed time. Finally, the application and comparison of the designed algorithm show that the algorithm can effectively solve the allocation problem of power resources such as economic dispatch.  相似文献   

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