Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty

A control strategy combining feedforward control and feedback control is presented for the optimal deployment of a spacecraft solar array system with the initial state uncertainty. A dynamic equation of the spacecraft solar array system is established under the assumption that the initial linear momentum and angular momentum of the system are zero. In the design of feedforward control, the dissipation energy of each revolute joint is selected as the performance index of the system. A Legendre pseudospectral method (LPM) is used to transform the optimal control problem into a nonlinear programming problem. Then, a sequential quadratic programming algorithm is used to solve the nonlinear programming problem and offline generate the optimal reference trajectory of the system. In the design of feedback control, the dynamic equation is linearized along the reference trajectory in the presence of initial state errors. A trajectory tracking problem is converted to a two-point boundary value problem based on Pontryagin’s minimum principle. The LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations which can be easily calculated. Then, the closed-loop state feedback control law is designed based on the resulting optimal feedback control and achieves good performance in real time. Numerical simulations demonstrate the feasibility and effectiveness of the proposed control strategy.     

三维电动力绳系子卫星轨道转移的最优控制

考虑复杂状态和控制约束的作用,研究了倾斜轨道上三维电动力绳系子卫星轨道转移的最优控制问题.借助Gauss伪谱算法,将绳系子卫星轨道转移的连续时间最优控制问题离散为大规模动态规划问题,并利用非线性规划方法进行求解.通过数值仿真计算了最优控制时间、子星最优转移轨道及最优控制张力和电流,同时讨论了轨道倾角对最优控制量的影响....     

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.     

最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间,针对平动点航天器编队重构的均衡耗能最优轨迹规划问题,提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解,并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域;同时,不需要对协态初值准确猜测,避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟,结果表明,本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标,具有一定的应用价值。     

Step-like contrast structure for class of nonlinear singularly perturbed optimal control problem

The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result.     

A multi-objective optimal PID control for a nonlinear system with time delay

It is generally difficult to design feedback controls of nonlinear systems with time delay to meet time domain specifications such as rise time, overshoot, and tracking error. Furthermore, these time domain specifications tend to be conflicting to each other to make the control design even more challenging. This paper presents a cell mapping method for multi-objective optimal feedback control design in time domain for a nonlinear Duffing system with time delay. We first review the multi-objective optimization problem and its formulation for control design. We then introduce the cell mapping method and a hybrid algorithm for global optimal solutions. Numerical simulations of the PID control are presented to show the features of the multi-objective optimal design.     

A minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems

A stochastic minimax optimal control strategy for partially observable uncertain quasi-Hamiltonian systems is proposed. First, the stochastic optimal control problem of a partially observable nonlinear uncertain quasi-Hamiltonian system is converted into that of a completely observable linear uncertain system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by a minimax optimal control strategy based on stochastic averaging method and stochastic differential game. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs (HJI) equation. As an example, the stochastic minimax optimal control of a partially observable Duffing–van der Pol oscillator with uncertain disturbances is worked out in detail to illustrate the procedure and effectiveness of the proposed control strategy.     

飞行时间不受约束的绳系卫星最优控制

研究了飞行时间不受约束的绳系卫星释放和回收过程的非线性最优控制问题.基于Chebyshev级数展开将高阶系统的状态约束和控制约束拟线性化,使问题转化成典型的线性二次规划问题,通过数值模拟验证了该方法的有效性,获得了绳系卫星轨道和控制力的时间最优历程.     

HYBRID OPTIMIZATION STRATEGY FOR MOTION PLANNING OF SPACE ROBOT SYSTEM WITH PRISMATIC JOINT

研究了自由漂浮带滑移铰空间机器人非完整运动规划的最优控制问题,提出一种由高斯伪谱法求解可行解与直接打靶法求解最优解相结合的混合优化策略.首先,根据多体系统动力学理论建立空间机器人的动力学模型,给定系统的初始和目标位形,将空间机器人运动规划问题描述成博尔察（Bolza）型最优控制问题;然后,利用高斯伪谱法将最优控制问题离散为非线性规划问题,求解在较少勒让德-高斯（Legendre-Gauss,LG）点时状态变量和控制变量对应的可行解;最后,在LG点处离散控制变量,作为直接打靶法的初值,利用序列二次规划算法求解空间机器人系统的优化运动轨迹和最优控制输入.通过数值仿真,系统优化运动轨迹光滑平稳,最优控制输入也能很好地满足各种约束条件,仿真结果验证了该混合优化策略的鲁棒性和有效性.     

Optimal control of nonlinear hydraulic networks in the presence of disturbance

Water leakage is an important component of water loss. Many methods have emerged from urban water supply systems for leakage control, but it still remains a challenge in many countries. Pressure management is an effective way to reduce the leakage in a system. It can also reduce the power consumption. To this end, an optimal control strategy is proposed in this paper. In the water supply system model, the hydraulic resistance of the valve is estimated by the real data from a water supply system and it is considered to be a disturbance. The method which is used to solve the nonlinear optimal control problem is the interior point method. The method which is used in this paper can be used for a general hydraulic networks to optimize the leakage and energy consumption and to satisfy the demands at the end-users.     

Based on wavelet analysis to optimal control of motion planning of space manipulator

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Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy

The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method(GPM) and direct shooting method(DSM) is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions.The results indicate that the method is effective with good robustness.     

基于微分包含的绳系卫星时间最优释放控制

考虑系绳弹性的影响,建立了绳系卫星系统三维动力学模型,研究了在状态和控制约束下的绳系卫星非线性时间最优控制问题. 为缩减系统变量,控制律设计没有采用通常的状态空间模型,而是基于二阶微分包含,将连续时间最优控制问题离散为大规模动态规化问题,最后通过数值模拟验证了该方法的有效性.      

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.     

Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.     

基于最优参数控制方法的齿轮系统混沌控制

基于最优参数控制方法,实现了齿轮传动系统中的混沌控制．以经典的间隙单齿轮副非线性动力学模型为研究对象,以啮合静载荷为控制参数,通过混沌吸引子中轨线的观测近似得到目标周期不动点、系统在目标不动点处的雅克比矩阵以及在控制原始参量处的梯度矩阵．最后运用最优参数控制策略计算得到啮合静载荷的小扰动量,实现了把齿轮系统的混沌运动镇定周期一轨道上的目的．研究结果表明,基于最优参数控制方法的控制过程,只是在控制的前几个周期内需要控制参数产生相对较大的扰动量,随着控制的继续进行,扰动量几乎稳定到了某一固定值,不再需要较大的变动．而且控制参数计算所需要的中间参量可以直接由混沌吸引子中轨线的观测近似得到,因而控制容易实现．     

Optimal bounded control for nonlinear stochastic smart structure systems based on extended Kalman filter

An optimal bounded control strategy for smart structure systems as controlled Hamiltonian systems with random excitations and noised observations is proposed. The basic dynamic equations for a smart structure system with smart sensors and actuators are firstly given. The nonlinear stochastic control system with noised observations is then obtained from the simplified smart structure system, and the system is expressed by generalized Hamiltonian equations with control, random excitation and dissipative forces. The optimal control problem for nonlinear stochastic systems with noised observations includes two parts: optimal state estimation and optimal response control based on estimated states, which are coupled each other. The probability density of optimally estimated systems has generally infinite dimensions based on the separation theorem. The proposed optimal control strategy gives an approximate separate solution. First, the optimally estimated system state is determined by the observations based on the extended Kalman filter, and the estimated nonlinear system with controls and stochastic excitations is obtained which has finite-dimensional probability density. Second, the dynamical programming equation for the estimated system is determined based on the stochastic dynamical programming principle. The control boundedness due to actuator saturation is considered, and the optimal bounded control law is obtained by the programming equation with the bounded control constraint. The optimal control depends on the estimated system state which is determined by noised observations. The proposed optimal bounded control strategy is finally applied to a single-degree-of-freedom nonlinear stochastic system with control and noised observation. The remarkable vibration control effectiveness is illustrated with numerical results. Thus the proposed optimal bounded control strategy is promising for application to nonlinear stochastic smart structure systems with noised observations.     

Symplectic multi-level method for solving nonlinear optimal control problem

By converting an optimal control problem for nonlinear systems to a Hamiltonian system,a symplecitc-preserving method is proposed.The state and costate variables are approximated by the Lagrange polynomial.The state variables at two ends of the time interval are taken as independent variables.Based on the dual variable principle,nonlinear optimal control problems are replaced with nonlinear equations.Furthermore,in the implementation of the symplectic algorithm,based on the 2N algorithm,a multilevel method is proposed.When the time grid is refined from low level to high level,the initial state and costate variables of the nonlinear equations can be obtained from the Lagrange interpolation at the low level grid to improve efficiency.Numerical simulations show the precision and the efficiency of the proposed algorithm in this paper.     

Optimal control of stretching process of solar arrays on spacecraft using wavelet expansion method

The optimal attitude control problem of spacecraft during its solar arrays stretching process is discussed in the present paper. By using the theory of wavelet analysis in control algorithm, the discrete orthonormal wavelet function is introduced into the optimal control problem, the method of wavelet expansion is substituted for the classical Fourier basic function. An optimal control algorithm based on wavelet analysis is proposed. The effectiveness of the wavelet expansion approach is shown by numerical simulation. This work is supported by the National Natural Science Foundation of China.     

Adaptive dynamic programming-based stabilization of nonlinear systems with unknown actuator saturation

This paper addresses the stabilizing control problem for nonlinear systems subject to unknown actuator saturation by using adaptive dynamic programming algorithm. The control strategy is composed of an online nominal optimal control and a neural network (NN)-based feed-forward saturation compensator. For nominal systems without actuator saturation, a critic NN is established to deal with the Hamilton–Jacobi–Bellman equation. Thus, the online approximate nominal optimal control policy can be obtained without action NN. Then, the unknown actuator saturation, which is considered as saturation nonlinearity by simple transformation, is compensated by employing a NN-based feed-forward control loop. The stability of the closed-loop nonlinear system is analyzed to be ultimately uniformly bounded via Lyapunov’s direct method. Finally, the effectiveness of the presented control method is demonstrated by two simulation examples.