Iterative Solution Methods for a Class of State and Control Constrained Optimal Control Problems

Iterative methods for solving discrete optimal control problems are constructed and investigated. These discrete problems arise when approximating by finite difference method or by finite element method the optimal control problems which contain a linear elliptic boundary value problem as a state equation, control in the righthand side of the equation or in the boundary conditions, and point-wise constraints for both state and control functions. The convergence of the constructed iterative methods is proved, the implementation problems are discussed, and the numerical comparison of the methods is executed.

基于ControlVAE的约束嵌入稠密时变阵列构建

在对探地雷达(Ground Penetrating Radar,GPR)数据进行三维建模与可视化分析过程中,其所依赖的三维时变阵列通常是由一维数据道或二维阵列间接生成的.由于采集到的数据往往比较稀疏,且存在不规则偏移,需要进行稠密处理,以获得高密度三维时变阵列.本文提出了一种基于可控变分自编码(Controllable Variational AutoEncoder,ControlVAE)的约束嵌入稠密时变阵列构建方法 .使用基于ControlVAE的时变数据重构网络,通过隐空间采样插值和深浅层特征信息的融合,生成接近真实分布的伪道数据来增加阵列密度.构建了基于尺度不变特征变换的数据配准模块,提取道间梯度特征与结构对称性特征,可以在时空域内完成数据配准.同时将浅层特征作为约束信息嵌入数据重构网络,以消除数据道偏移对阵列生成的影响.实验结果表明,本文方法仅使用单测线二维B-scan数据集即可重建稠密时变阵列,可以有效降低重构模型累积误差,提高面对复杂真实数据时的鲁棒性.

Disturbance rejection tube model predictive levitation control of maglev trains

Magnetic levitation control technology plays a significant role in maglev trains.Designing a controller for the levitation system is challenging due to the strong nonlinearity,open-loop instability,and the need for fast response and security.In this paper,we propose a Disturbance-Observe-based Tube Model Predictive Levitation Control(DO-TMPLC)scheme combined with a feedback linearization strategy for the levitation system.The proposed strategy incorporates state constraints and control input constraints,i.e.,the air gap,the vertical velocity,and the current applied to the coil.A feedback linearization strategy is used to cancel the nonlinearity of the tracking error system.Then,a disturbance observer is implemented to actively compensate for disturbances while a TMPLC controller is employed to alleviate the remaining disturbances.Furthermore,we analyze the recursive feasibility and input-to-state stability of the closed-loop system.The simulation results indicate the efficacy of the proposed control strategy.

Sub-Time-Optimal Control of Constrained Nonlinear Systems

To reduce the number of the level sets used in algorithm of constrained nonlinear systems via ellipsoidal techniques, according to the analysis of mathematics, searching algorithm is used for choosing the control input. Simulation shows that the number of level sets used for controlling is almost the same as that used in polytope techniques. Sub time optimal algorithm reduces the number of the level sets used in ellipsoidal techniques.

Active Vibration Control of Beam Using Electro-magnetic Constrained Layer Damping

This paper investigates vibration control of beam through electro-magnetic constrained layer damping （EMCLD） which consists of electromagnet layer, permanent magnet layer and viscoelastic damping layer. When the coil of the electromagnet is electrified with proper control strategy, the electromagnet can exert magnetic force opposite to the direction of structural deformation so that the structural vibration is attenuated. A mathematical model is developed based on the equivalent current method to calculate the electromagnetic control force produced by EMCLD. The governing equations of the system are obtained using Hamilton＇s Principle and then reduced with the assumed-mode method. A simulation on vibration control of a cantilever beam is conducted under the velocity proportional feedback to demonstrate the energy dissipation capability of EMCLD, and the beam system with the same parameter is experimented. The results of experiment and simulation are compared and the results show that the EMCLD is an effective means for suppressing modal vibration. The results also indicate that the beam system has better control performance for larger control current. The EMCLD method presented in this paper provides an applicable and efficient tool for the vibration control of structures.

A Dual-mode Nonlinear Model Predictive Control with the Enlarged Terminal Constraint Sets

Aiming at a class of nonlinear systems with multiple equilibrium points, we present a dual-mode model predictive control algorithm with extended terminal constraint set combined with control invariant set and gain schedule. Local LQR control laws and the corresponding maximum control invariant sets can be designed for finite equilibrium points. It is guaranteed that control invariant sets are overlapped each other. The union of the control invariant sets is treated as the terminal constraint set of predictive control. The feasibility and stability of the novel dual-mode model predictive control are investigated with both variable and fixed horizon. Because of the introduction of extended terminal constrained set, the feasibility of optimization can be guaranteed with short prediction horizon. In this way, the size of the optimization problem is reduced so it is computationally efficient. Finally, a simulation example illustrating the algorithm is presented.

Time-Varying Asymmetrical BLFs Based Adaptive Finite-Time Neural Control of Nonlinear Systems With Full State Constraints

This paper concentrates on asymmetric barrier Lyapunov functions(ABLFs)based on finite-time adaptive neural network(NN)control methods for a class of nonlinear strict feedback systems with time-varying full state constraints.During the process of backstepping recursion,the approximation properties of NNs are exploited to address the problem of unknown internal dynamics.The ABLFs are constructed to make sure that the time-varying asymmetrical full state constraints are always satisfied.According to the Lyapunov stability and finitetime stability theory,it is proven that all the signals in the closedloop systems are uniformly ultimately bounded(UUB)and the system output is driven to track the desired signal as quickly as possible near the origin.In the meantime,in the scope of finitetime,all states are guaranteed to stay in the pre-given range.Finally,a simulation example is proposed to verify the feasibility of the developed finite time control algorithm.

Neural adaptive chaotic control with constrained input using state and output feedback

This paper presents neural adaptive control methods for a class of chaotic nonlinear systems in the presence of constrained input and unknown dynamics. To attenuate the influence of constrained input caused by actuator saturation, an effective auxiliary system is constructed to prevent the stability of closed loop system from being destroyed. Radial basis function neural networks（RBF-NNs） are used in the online learning of the unknown dynamics, which do not require an off-line training phase. Both state and output feedback control laws are developed. In the output feedback case, high-order sliding mode（HOSM） observer is utilized to estimate the unmeasurable system states. Simulation results are presented to verify the effectiveness of proposed schemes.

Saturated Adaptive Output-Constrained Control of Cooperative Spacecraft Rendezvous and Docking

This paper investigates the robust relative pose control for spacecraft rendezvous and docking with constrained relative pose and saturated control inputs.A barrier Lyapunov function is used to ensure the constraints of states,so that the computational singularity of the inverse matrix in control command can be avoided,while a linear auxiliary system is introduced to handle with the adverse effect of actuator saturation.The tuning rules for designing parameters in control command and auxiliary system are derived based on the stability analysis of the closed-loop system.It is proved that all closed-loop signals always keep bounded,the prescribed constraints of relative pose tracking errors are never violated,and the pose tracking errors ultimately converge to small neighborhoods of zero.Simulation experiments validate the performance of the proposed robust saturated control strategy.

Identification and nonlinear model predictive control of MIMO Hammerstein system with constraints

This work is concerned with identification and nonlinear predictive control method for MIMO Hammerstein systems with constraints. Firstly, an identification method based on steady-state responses and sub-model method is introduced to MIMO Hammerstein system. A modified version of artificial bee colony algorithm is proposed to improve the prediction ability of Hammerstein model. Next, a computationally efficient nonlinear model predictive control algorithm(MGPC) is developed to deal with constrained problem of MIMO system. The identification process and performance of MGPC are shown. Numerical results about a polymerization reactor validate the effectiveness of the proposed method and the comparisons show that MGPC has a better performance than QDMC and basic GPC.

Constrained Control of Interpolating Surfaces by Parameters

In order to meet the needs of practical design, an interpolation technique is employed to constrain the shape of surfaces. The method of preserving positivity on the interpolation surface and constraint on interpolating data is also developed. The advantage of this new method is that it can be used to constrain the shape of an interpolating surface only by selecting suitable parameters, and numerical examples are presented to show the performance of the method.

MULTI-LAYER PIEZOELECTRIC ACTUATOR AND ITS APPLICATION IN CONTROLLABLE CONSTRAINED DAMPING TREATMENT

A kind of novel multi-layer piezoelectric actuator is proposed and integrated with controllable constrained damping treatment to perform hybrid vibration control. The governing equation of the system is derived based on the constitutive equations of elastic, viscoelastic and piezoelectric materials, which shows that the magnitude of control force exerted by multi-layer piezoelectric actuator is the quadratic function of the number of piezoelectric laminates used but in direct proportion to control voltage. This means that the multi-layer actuator can produce greater actuating force than that by piezoelectric laminate actuator with the same area under the identical control voltage. The optimal location placement of the multi-layer piezoelectric actuator is also discussed. As an example, the hybrid vibration control of a cantilever rectangular thin-plate is numerically simulated and carried out experimentally. The simulated and experimental results validate the power of multi-layer piezoelectric actuator and indicate that the present hybrid damping technique can effectively suppress the low frequency modal vibration of the experimental thin-plate structure.

Constrained sliding mode control of nonlinear fractional order input affine systems

Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.

A STA Current-Constrained Control for PMSM Speed Regulation System with Function Disturbance Observer

The non-cascade permanent magnet synchronous motor control system has the advantages of simple structure and less adjustable parameters,but the non-cascade structure needs to solve the problem of over-current protection.In this paper,a current constrained control method is used to limit the starting current to a safe range.At the same time,to ensure the robustness and rapidity of the system,a super twist current constraint controller(CCSTA)is generated by combining super twist algorithm(STA)with current constraint control;Considering the diversity of internal and external disturbances,a functional disturbance observer(FDOB)is proposed to compensate the matched and unmatched disturbances,which further improves the robustness of the system.

Receding horizon H_∞ control for constrained time-delay systems

A receding horizon Hoo control algorithm is presented for linear discrete time-delay system in the presence of constrained input and disturbances. Disturbance attenuation level is optimized at each time instant, and the receding optimization problem includes several linear matrix inequality constraints. When the convex hull is applied to denote the saturating input, the algorithm has better performance. The numerical example can verify this result.

Decentralized adaptive neural network sliding mode position/force control of constrained reconfigurable manipulators

A decentralized adaptive neural network sliding mode position/force control scheme is proposed for constrained reconfigurable manipulators. Different from the decentralized control strategy in multi-manipulator cooperation, the proposed decentralized position/force control scheme can be applied to series constrained reconfigurable manipulators. By multiplying each row of Jacobian matrix in the dynamics by contact force vector, the converted joint torque is obtained. Furthermore, using desired information of other joints instead of their actual values, the dynamics can be represented as a set of interconnected subsystems by model decomposition technique. An adaptive neural network controller is introduced to approximate the unknown dynamics of subsystem. The interconnection and the whole error term are removed by employing an adaptive sliding mode term. And then, the Lyapunov stability theory guarantees the stability of the closed-loop system. Finally, two reconfigurable manipulators with different configurations are employed to show the effectiveness of the proposed decentralized position/force control scheme.

Analytic Solutions to Optimal Control Problems with Constraints

In this paper, the analytic solutions to constrained optimal control problems are considered. A novel approach based on canonical duality theory is developed to derive the analytic solution of this problem by reformulating a constrained optimal control problem into a global optimization problem. A differential flow is presented to deduce some optimality conditions for solving global optimizations, which can be considered as an extension and a supplement of the previous results in canonical duality theory. Some examples are given to illustrate the applicability of our results.

VIBRATION CONTROL OF FLUID-FILLED PRISMATIC SHELL WITH ACTIVE CONSTRAINED LAYER DAMPING TREATMENTS

Active constrained layer damping （ACLD） combines the simplicity and reliability of passive damping with the light weight and high efficiency of active actuators to obtain high damping over a wide frequency band. A fluid-filled prismatic shell is set up to investigate the validity and efficiency of ACLD treatments in the case of fluid-structure interaction. By using state subspace identification method, modal parameters of the ACLD system are identified and a state space model is established subsequently for the design of active control laws. Experiments are conducted to the fluid-filled prismatic shell subjected to random and impulse excitation, respectively, For comparison, the shell model without fluid interaction is experimented as well. Experimental results have shown that the ACLD treatments can suppress vibration of the fluid-free and fluid-filled prismatic shell effectively. Under the same control gain, vibration attenuation is almost the same in both cases.

Symplectic Numerical Approach for Nonlinear Optimal Control of Systems with Inequality Constraints

This paper proposes a system representation for unifying control design and numerical calculation in nonlinear optimal control problems with inequality constraints in terms of the symplectic structure. The symplectic structure is derived from Hamiltonian systems that are equivalent to Hamilton-Jacobi equations. In the representation, the constraints can be described as an input-state transformation of the system. Therefore, it can be seamlessly applied to the stable manifold method that is a precise numerical solver of the Hamilton-Jacobi equations. In conventional methods, e.g., the penalty method or the barrier method, it is difficult to systematically assign the weights of penalty functions that are used for realizing the constraints. In the proposed method, we can separate the adjustment of weights with respect to objective functions from that of penalty functions. Furthermore, the proposed method can extend the region of computable solutions in a state space. The validity of the method is shown by a numerical example of the optimal control of a vehicle model with steering limitations.