Discrete optimal control for Birkhoffian systems

In this paper, we investigate a discrete variational optimal control for mechanical systems that admit a Birkhoffian representation. Instead of discretizing the original equations of motion, our research is based on a direct discretization of the Pfaff–Birkhoff–d’Alembert principle. The resulting discrete forced Birkhoffian equations then serve as constraints for the minimization of the objective functional. In this way, the optimal control problem is transformed into a finite-dimensional optimization problem, which can be solved by standard methods. This approach yields discrete dynamics, which is more faithful to the continuous equations of motion and consequently yields more accurate solutions to the optimal control problem which is to be approximated. We illustrate the method numerically by optimizing the control for the damped oscillator.     

The planning of optimal motions of non-holonomic systems

Nonlinear Dynamics - A new method to the planning of optimal motions of the non-holonomic systems is presented. It is based on a non-classical formulation of the Pontryagin Maximum Principle given...     

H 2 optimal filtering for bilinear systems

The filtering problem is among the fundamental issues in control and signal processing. Several approaches such as H ₂ optimal filtering and H _?? optimal filtering have been developed to address this issue. While the optimal H ₂ filtering problem has been extensively studied in the past for linear systems, to the best of our knowledge, it has not been studied for bilinear systems. This is indeed surprising, since bilinear systems are important class of nonlinear systems with well-established theories and applications in various fields. The problem of H ₂ optimal filtering for both discrete-time and continuous bilinear systems is addressed in this paper. The filter design problem is formulated in the optimization framework. The problem for the discrete-time case is expressed in terms of linear matrix inequalities which can be efficiently solved. The results are used for the optimal filtering of a bilinear model of an electro-hydraulic drive.     

Canonical transformations in the optimal control of mechanical systems

In this paper the canonical perturbation method, which is widely used in analytical mechanics, is applied to optimal control problems. It is shown that the state and adjoint equations present additional interesting symmetries if the state equations are themselves of the Hamiltonian type, which is frequently the case if a mechanical system is to be controlled. The application of the canonical perturbation method to optimal control problems turns out to be particularly simple, if the optimal control is piecewise constant. Several examples are considered.     

参数摄动H∞滤波系统的最优性能指标计算

基于H∞滤波系统的最优性能指标与相应的Hamilton微分方程特征值之间的对应关系,利用微分方程特征值的摄动法研究了参数摄动H∞滤波系统的性能指标计算问题。当原滤波系统的最优性能指标已知时,利用系统参数的变化量就可以确定摄动系统的最优性能指标。     

线性时滞系统的离散最优控制

介绍了对线性时滞系统进行最优控制的设计,将具有时滞控制的线性系统离散后引入增广状态向量。获得不显含时滞的差分方程,根据时滞量的两种分类情况采用连续和离散形式的性能指标函数导出了最优控制律。控制律包含当前状态和此前若干步状态向量的叠加,最优控制律直接从时滞方程中得到,可保证系统的稳定性,此方法亦适用于大时滞的情况。数值算例验证了控制策略的有效性。     

Cooperative game-oriented optimal design in constraint-following control of mechanical systems

Nonlinear Dynamics - This paper proposes a cooperative game-oriented optimal design problem of robust control for uncertain mechanical systems. State of the concerned system is affected by...     

Nonlinear optimal control of population systems: applications in ecosystems

This article investigates the chaotic Lotka–Volterra system as an optimal nonlinear design problem for biological pest control strategies. In the biological control strategy, natural enemies are introduced such that the pest density is stabilized below the economic injury level, and the population of natural enemies remains sufficiently high to control the pests. Applying dynamic programming, this problem was reduced to the Hamilton–Jacobi–Bellman equation. The functions satisfying the reduced equation were obtained among the correspondent Lyapunov functions of the considered Lotka–Volterra system. A closed-form optimal feedback control law was derived. The effectiveness of the method is verified by numerical simulations of biological pest control. The biological implications of these results are also discussed.     

A compressed-sensing approach for closed-loop optimal control of nonlinear systems

We present a method that seeks to combine the properties of optimal control with the robust character of closed-loop control. The method relies on the availability of a reduced model of the system to be controlled, in order to express the control problem in a low-dimensional space where the system-state-dependent optimal control law is subsequently approximated in a preprocessing stage. A polynomial expansion is used for the approximation, enabling fast update of the optimal control law each time a new observation of the system state is made available. It results in a real-time compatible, efficient (optimal-like), and robust control strategy. A compressed-sensing approach is proposed to efficiently construct the approximate control law, exploiting the compressible character of the optimal control law in the retained approximation basis. The method is demonstrated for the control of the flow around a cylinder and is shown to perform as well as the much more costly receding-horizon optimal control approach, where the exact optimal control problem is actually recomputed, even in the presence of large aleatoric perturbations. Potential and remaining issues toward application to larger dimensional reduced systems are also discussed, and some directions for improvement are suggested.     

Symmetry classification and optimal systems of a non-linear wave equation

In this paper the complete Lie group classification of a non-linear wave equation is obtained. Optimal systems and reduced equations are achieved in the case of a hyperelastic homogeneous bar with variable cross section.     

Dynamic analysis and optimal control of drag-based vibratory systems using averaging

Nonlinear Dynamics - This paper presents dynamic analysis and optimal control of vibratory systems with asymmetric drag and asymmetric added mass, moving in a resisting medium. The paper considers...     

The optimal truncated low-dimensional dynamical systems based on flow databases

A new theory on the construction of optimal truncated Low-Dimensional Dynamical Systems (LDDSs) with different physical meanings has been developed. The physical properties of the optimal bases are reflected in the user-defined optimal conditions. Through the analysis of linear and nonlinear examples, it is shown that the LDDSs constructed by using the Proper Orthogonal Decomposition (POD) method are not the optimum. After comparing the errors of LDDSs based on the new theory, POD and Fourier methods, it is concluded that the LDDSs based on the new theory are optimally truncated and catch the desired physical properties of the systems. The project supported by the National Natural Science Foundation of China and LNM, Institute of Mechanics, CAS     

SDRE-based near optimal nonlinear controller design for unified chaotic systems

This paper proposes a near optimal controller design method for unified chaotic systems based on state-dependent Riccati equation (SDRE) approach. A parameterization of the optimal nonlinear control gain is given in terms of the solution matrix of an SDRE. A simple algorithm to compute the near optimal control gain is proposed. The proposed near optimal control design method is also extended to the synchronization problem for unified chaotic systems. Finally, the effectiveness of the proposed design method is verified via numerical simulations.     

Data-driven-based event-triggered optimal control of unknown nonlinear systems with input constraints

Nonlinear Dynamics - This paper is concerned with event-triggered control problem for unknown nonlinear systems with input constraints. By introducing a nominal system and a discounted cost...     

Stochastic optimal bounded control of MDOF quasi nonintegrable-Hamiltonian systems with actuator saturation

A new bounded optimal control strategy for multi-degree-of-freedom (MDOF) quasi nonintegrable-Hamiltonian systems with actuator saturation is proposed. First, an n-degree-of-freedom (n-DOF) controlled quasi nonintegrable-Hamiltonian system is reduced to a partially averaged Itô stochastic differential equation by using the stochastic averaging method for quasi nonintegrable-Hamiltonian systems. Then, a dynamical programming equation is established by using the stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang–bang control is derived. Finally, the response of the optimally controlled system is predicted by solving the Fokker–Planck–Kolmogorov (FPK) equation associated with the fully averaged Itô equation. An example of two controlled nonlinearly coupled Duffing oscillators is worked out in detail. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and that chattering is reduced significantly compared with the bang–bang control strategy.     

The optimal control of delay control systems with restricted state right endpoint

I.'Introducti0nInthecontroltheory,theresoIutionofoptimalcontrolpr0blems,especiallythePontryaginmaximumprinciple,hasaffordedveryusefuIto0lsfortheadvanceofmodernscienceandthepracticalsystemssuchasthesystemsofmechanica1,economicadministrational,industrialand…     

Dynamics and optimal control of multibody systems using fractional generalized divide-and-conquer algorithm

In this paper, a new framework is presented for the dynamic modeling and control of fully actuated multibody systems with open and/or closed chains as well as disturbance in the position, velocity, acceleration, and control input of each joint. This approach benefits from the computed torque control method and embedded fractional algorithms to control the nonlinear behavior of a multibody system. The fractional Brunovsky canonical form of the tracking error is proposed for a generalized divide-and-conquer algorithm (GDCA) customized for having a shortened memory buffer and faster computational time. The suite of a GDCA is highly efficient. It lends itself easily to the parallel computing framework, that is used for the inverse and forward dynamic formulations. This technique can effectively address the issues corresponding to the inverse dynamics of fully actuated closed-chain systems. Eventually, a new stability criterion is proposed to obtain the optimal torque control using the new fractional Brunovsky canonical form. It is shown that fractional controllers can robustly stabilize the system dynamics with a smaller control effort and a better control performance compared to the traditional integer-order control laws.

     

Analysis for the optimal location of cable damping systems on stayed bridges

Computational models are increasingly being used for the dynamic analysis of structures with nonlinear or uncertain behavior, such as cables in stayed bridges, which nowadays are progressively more used as an alternative for long span and slim structures. In this work, a 3D nonlinear model is described to evaluate the wind dynamic effects on cables for this type of bridges under different scenarios, but also for health monitoring and structural simulation to guarantee performance, evaluate load capacity and estimate life prediction. Fatigue is one of the most relevant and complex failure causes in highway bridges, particularly on the anchorage elements of the cables in stayed bridges; where dampers may be used to minimize the dynamic behavior of the structure and reduce fatigue damage. With this nonlinear simulation model, different damper locations and configurations are evaluated to find the optimal position. A feasibility function is used as a weighting function to take into account the damper’s size and design. Analysis is particularly focused for a real cable stayed bridge in the state of Veracruz in México. Although the geometry, the forces and the stresses on cable structures are a challenge, even for structural specialists, the results from this work using the proposed 3D nonlinear model showed to be accurate for the simulation of many different wind scenarios, and damper’s location and orientations. Finally, the feasibility weighting function enabled the geometrical limitations to estimate the best location of a damper system to minimize the risk for fatigue failure.