Statistical information based two-layer model predictive control with dynamic economy and control performance for non-Gaussian stochastic process

In this paper, a two-layer model predictive control (MPC) hierarchical architecture of dynamic economic optimization (DEO) and reference tracking (RT) is proposed for non-Gaussian stochastic process in the framework of statistical information. In the upper layer, with state feedback and dynamic economic information, the economically optimal trajectories are estimated by entropy and mean based dynamic economic MPC, which uses the nonlinear dynamic model instead of the steady-state model. These estimated optimal trajectories from the upper layer are then employed as the reference trajectories of the lower layer control system. A survival information potential based MPC algorithm is used to maintain the controlled variables at their reference trajectories in the nonlinear system with non-Gaussian disturbances. The stability condition of closed-loop system dynamics is proved using the statistical linearization method. Finally, a numerical example and a continuous stirred-tank reactor are used to illustrate the merits of the proposed economic optimization and control method.     

Event triggered model predictive control: A less conservative result

This paper studies the event-triggered model predictive control (MPC) of a stabilizable linear continuous-time system. The optimization problem associated with the proposed MPC strategy is formulated exploiting newly designed control constraints. Compared with the conventional tube-based MPC, where the constant tightened control constraints are employed, the proposed MPC strategy exploits the time-varying control constraints, which allows the control signal to take larger values in the beginning along the prediction horizon, resulting in potentially improved system performance. The re-computation of the control signal is triggered by the deviation of the predicted system state and the real system state. Furthermore, conditions are derived based on which the design parameters can be tuned to ensure the recursive feasibility of the optimization and the stability of the closed-loop system. Finally, the effectiveness of the proposed MPC strategy is verified using a numerical example.     

Interval type-2 T-S fuzzy MPC for CPS under hybrid attacks over a multi-channel framework

In this paper, the problem of observer-based model predictive control (MPC) for a multi-channel cyber-physical system (CPS) with uncertainties and hybrid attacks is investigated via interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model. Both denial-of-service (DoS) and false data injection (FDI) attacks are studied due to the vulnerability of wireless transmission channels. The objective of the addressed problem is to improve the security performance of the multi-channel CPS under malicious attacks, which has not been adequately investigated in the existing MPC algorithms. Moreover, uncertainties which appear not only in the membership functions but in both state and input matrices are considered. In this paper, different from the method that FDI attacks are handled by the bounded functions, an off-line observer is designed to actively defend against the FDI attacks. Meanwhile, an on-line MPC optimization algorithm, which minimizes the upper bound of objective function respecting input constraints, is presented to obtain the secure controller gains. Finally, an illustrative example is provided to verify the effectiveness and superiority of presented approach.     

Fault-tolerant tracking control based on reinforcement learning with application to a steer-by-wire system

In this paper, a novel complete model-free integral reinforcement learning (CMFIRL) algorithm based fault tolerant control scheme is proposed to solve the tracking problem of steer-by-wire (SBW) system. We begin with the recognition that the reference errors can eventually converge to zero based on the command generator model. Then an augmented tracking system is constructed with a corresponding performance index which is considered as a type of actuator failure. By using the reinforcement learning (RL) technique, three novel online update strategies are respectively developed to cope with the following three cases, i.e., model-based, partially model-free, and completely model-free. Especially, the RL algorithm for the complete model-free case eliminates the constraints of requiring the known system dynamics in fault-tolerant tracking controlling. The system stability and the convergence of the CMFIRL iteration algorithm are also rigorously proved. Finally, a simulation example is given to illustrate the effectiveness of the proposed approach.     

High-order fully actuated system approaches: Model predictive control with applications to under-actuated systems

The main results of this paper are concentrated on the nonlinear model predictive control (MPC) tracking optimization based on high-order fully actuated (HOFA) system approaches. The proposed HOFA MPC strategy makes full use of full-actuation property to eliminate the nonlinear dynamics of the system, and then the nonlinear optimization problem is equivalently transformed into a series of easy-solve linear convex optimization problems. Different from general nonlinear MPC methods and the current optimal control of the HOFA system approach, an analytical controller with smooth and less energy is obtained by the moving horizon optimization. And it is proven that the proposed controller can stabilize the corresponding tracking error closed-loop system. Finally, not limited to FA systems, as examples, a nonlinear numerical under-actuated model in the mathematical sense and a benchmark nonlinear under-actuated mechanical system are transformed into corresponding equivalent HOFA systems, the simulation results are given to verify the effectiveness of the proposed strategy.     

Automatic parking trajectory planning based on random sampling and nonlinear optimization

The current parking trajectory planning algorithms based on geometric connections or formulation of optimization problems in automatic parking systems have strict requirements on the starting position, lower planning efficiency and discontinuous curvature of the reference trajectory. In order to solve these problems, a hierarchical planning algorithm which is combined with nonlinear optimization and the improved RRT* algorithm (Rapidly-exploring Random Tree Star) with Reeds-Shepp curve is proposed in this paper. First, the improved RRT*RS algorithm with the rapid repulsion-straddle experiment is designed for enhancing the efficiency of path planning. Second, because of the shortcomings of the Reeds-Shepp curve that can meet the minimum turning radius but not realize the continuous curvature of the path, a nonlinear optimization problem based on convex-set obstacle constraints is formulated and solved. Finally, simulation results show that the proposed parking trajectory planning algorithm in this paper can plan an effective parking trajectory with continuous curvature in different starting positions and multiple parking scenarios.     

Quadcopter formation flight control combining MPC and robust feedback linearization

This paper presents an integrated and practical control strategy to solve the leader–follower quadcopter formation flight control problem. To be specific, this control strategy is designed for the follower quadcopter to keep the specified formation shape and avoid the obstacles during flight. The proposed control scheme uses a hierarchical approach consisting of model predictive controller (MPC) in the upper layer with a robust feedback linearization controller in the bottom layer. The MPC controller generates the optimized collision-free state reference trajectory which satisfies all relevant constraints and robust to the input disturbances, while the robust feedback linearization controller tracks the optimal state reference and suppresses any tracking errors during the MPC update interval. In the top-layer MPC, two modifications, i.e. the control input hold and variable prediction horizon, are made and combined to allow for the practical online formation flight implementation. Furthermore, the existing MPC obstacle avoidance scheme has been extended to account for small non-apriorily known obstacles. The whole system is proved to be stable, computationally feasible and able to reach the desired formation configuration in finite time. Formation flight experiments are set up in Vicon motion-capture environment and the flight results demonstrate the effectiveness of the proposed formation flight architecture.     

Quasi-min–max MPC for constrained nonlinear systems with guaranteed input-to-state stability

This paper presents a robust quasi-min–max model predictive control algorithm for a class of nonlinear systems described by linear parameter varying (LPV) systems subject to input constraints and unknown but bounded disturbances. The proposed control algorithm solves a semi-definite programming problem that explicitly incorporates a finite horizon cost function and linear matrix inequalities (LMI) constraints. For the purpose of the recursive feasibility of the optimization, the dual-mode approach is implied. Input-to-state stability (ISS) and quasi-min–max MPC are combined to achieve the closed-loop ISS of the controller with respect to the disturbance in LMI paradigm. Two examples of continuous stirred tank reactor (CSTR) and couple-mass-spring system are used to demonstrate the effectiveness of the proposed results.     

Distributed optimization with information-constrained population dynamics

In a multi-agent framework, distributed optimization problems are generally described as the minimization of a global objective function, where each agent can get information only from a neighborhood defined by a network topology. To solve the problem, this work presents an information-constrained strategy based on population dynamics, where payoff functions and tasks are assigned to each node in a connected graph. We prove that the so-called distributed replicator equation (DRE) converges to an optimal global outcome by means of the local-information exchange subject to the topological constraints of the graph. To show the application of the proposed strategy, we implement the DRE to solve an economic dispatch problem with distributed generation. We also present some simulation results to illustrate the theoretic optimality and stability of the equilibrium points and the effects of typical network topologies on the convergence rate of the algorithm.     

Robust augmented complex-valued normalized M-estimate subband adaptive filtering algorithm against colored non-circular inputs and impulsive noise

Recently, the augmented complex-valued normalized subband adaptive filtering (ACNSAF) algorithm has been proposed to process colored non-circular signals. However, its performance will deteriorate severely under impulsive noise interference. To overcome this issue, a robust augmented complex-valued normalized M-estimate subband adaptive filtering (ACNMSAF) algorithm is proposed, which is obtained by modifying the subband constraints of the ACNSAF algorithm using the complex-valued modified Huber (MH) function and is derived based on CR calculus and Lagrange multipliers. In order to improve both the convergence speed and steady-state accuracy of the fixed step size ACNMSAF algorithm, a variable step size (VSS) strategy based on the minimum mean squared deviation (MSD) criterion is devised, which allocates individual adaptive step size to each subband, fully exploiting the structural advantages of SAF and significantly improving the convergence performance of the ACNMSAF algorithm as well as its tracking capability in non-stationary environment. Then, the stability, transient and steady-state MSD performance of the ACNMSAF algorithm in the presence of colored non-circular inputs and impulsive noise are analyzed, and the stability conditions, transient and steady-state MSD formulas are also derived. Computer simulations in impulsive noise environments verify the accuracy of theoretical analysis results and the effectiveness of the proposed algorithms compared to other existing complex-valued adaptive algorithms.     

Solving a reliability-performance balancing problem for control systems with degrading actuators under model predictive control framework

In this paper, we formulate and study a reliability-performance balancing problem (RPBP) for long-term operational and unattended control systems with degrading actuators. It preliminarily explores a new type of autonomous maintenance method to extend the useful lifetime of the control system. The actuator, as the crucial component of a control system, executes calculated control actions and thereby is often exposed to the high-load working environment. As the actuator degrades, the control action will gradually alter with increasing magnitude to maintain the desired control performance, but this will accelerate the actuator degradation and thus reduce the useful lifetime (use reliability) of the control system. Therefore, conditionally balancing the control performance and use reliability is meaningful, for which a novel dynamic regulation strategy under the model predictive control (MPC) framework is proposed. Specifically, we model the actuator degradation using a diffusion Wiener process coupled with the control action or system state, and the corresponding actuator reliability is derived. By fusing the degradation model and system dynamics, a degradation-incorporated state space (DISS) model is formulated, in which the basic idea is to consider the actuator degradation as an extended state variable and to control it accordingly. Based on the DISS model, a mixed-index nonlinear MPC integrated with a weight tuning strategy is proposed to achieve a satisfactory balance between control performance and use reliability in the presence of actuator degradation. Further, the reference curve and the upper bound of actuator degradation are given for constructing the objective function and the constraint in the MPC optimization problem. An illustrative example is presented to demonstrate the availability of the proposed method.     

Conjugate gradient-based FLANN algorithms in nonlinear active noise control

The conjugate gradient (CG) method exhibits fast convergence speed than the steepest descent, which has received considerable attention. In this work, we propose two CG-based methods for nonlinear active noise control (NLANC). The proposed filtered-s Bessel CG (FsBCG)-I algorithm implements the functional link artificial neural network (FLANN) as a controller, and it is derived from the Matérn kernel to achieve enhanced performance in various environments. On the basis of the FsBCG-I algorithm, we further develop the FsBCG-II algorithm, which utilizes the Bessel function of the first kind to constrain outliers. As an alternative, the FsBCG-II algorithm has reduced computational complexity and similar performance as compared to the FsBCG-I algorithm. Moreover, the convergence property of the algorithms is analyzed. The proposed algorithms are compared with some highly cited previous works. Extensive simulation results demonstrate that the proposed algorithms can achieve robust performance when the noise source is impulsive, Gaussian, logistic, and time-varying.     

Dynamic event-triggered optimal tracking control for constrained nonlinear stochastic systems

This paper investigates the optimal tracking control problem (OTCP) for nonlinear stochastic systems with input constraints under the dynamic event-triggered mechanism (DETM). Firstly, the OTCP is converted into the stabilizing optimization control problem by constructing a novel stochastic augmented system. The discounted performance index with nonquadratic utility function is formulated such that the input constraint can be encoded into the optimization problem. Then the adaptive dynamic programming (ADP) method of the critic-only architecture is employed to approximate the solutions of the OTCP. Unlike the conventional ADP methods based on time-driven mechanism or static event-triggered mechanism (SETM), the proposed adaptive control scheme integrates the DETM to further lighten the computing and communication loads. Furthermore, the uniform ultimately boundedness (UUB) of the critic weights and the tracking error are analysed with the Lyapunov theory. Finally, the simulation results are provided to validate the effectiveness of the proposed approach.     

Lexicographic MPC with multiple economic criteria for constrained nonlinear systems

Many control problems in process systems feature multi-objective optimization problems that involve several and often conflicting objective functions, such as economic profit and environmental concerns. In this paper, we consider a class of multi-objective model predictive control (MO-MPC) problems where nonlinear systems are subject to state and control constraints and multiple economic criteria are conflicting. Using the lexicographic optimization, we propose a prioritized MO-MPC scheme with guaranteed stability for economic optimization. At each sampling time, the MPC action is computed by solving a set of sequentially ordered single objective optimized control problems. Some sufficient conditions are established to ensure recursive feasibility and asymptotic stability of the MO-MPC in the context of economic criteria optimization. Two examples of multi-objective control of a coupled-tank system and a free-radical polymerization process are exploited to illustrate the effectiveness of the proposed MPC scheme and to evaluate the performance by some comparison experiments.     

Robust tube-based MPC with enlarging the region of attraction for tracking of switched systems

This paper addresses a robust tube based model predictive control (RTBMPC) strategy for tracking problem of piecewise affine (PWA) linear systems. The core idea of the RTBMPC strategy is to robustly control an uncertain system through its nominal system and an additional feedback term which rejects a bounded additive disturbance. In tracking problem, RTBMPC strategy should be capable to steer the uncertain system to a given setpoint fulfilling the constraints. But if the setpoint changes, the controller may not success due to the loss of feasibility of the optimization problem. This paper employs several novel features to deal with tracking problem. First, the tracking problem is converted into the regulation problem by introducing an extra system called regulation nominal system that its constraints are translated from tracking into regulation. It leads to a reduction in complexity of the objective function. Then, the feasibility region is enlarged for given setpoint without increasing the prediction horizon by changing the terminal constraint set at different steps of RTBMPC problem solving. Simulation examples, including two different case studies, are presented to illustrate the effectiveness of the proposed RTBMPC.     

Measurement outlier-Resistant target tracking in wireless sensor networks with energy harvesting constraints

In this paper, the measurement outlier-resistant target tracking problem is investigated in wireless sensor networks (WSNs) with energy harvesting constraints. Each WSN node can acquire energy stochastically from surroundings. No matter whether the WSN node acquires energy or not, the WSN node’s measurement can be transmitted if the energy amount of the WSN node is greater than zero. In such a case, the sensor energy-induced missing measurement (SE-IMM) phenomenon may occur. The objective of this paper is to develop a solution for the considered target tracking problem by devising the filter including a saturation constraint such that, in the simultaneous presence of outliers and the SE-IMM phenomenon, the tracking performance can meet the given performance index. Firstly, the relation between the energy level of the WSN node and its probability distribution is computed recursively. Then, an upper bound of the tracking error covariance is derived which is minimized by appropriately choosing the filter parameter. Finally, the feasibility of the proposed target tracking scheme is validated by conducting a set of comparative experiments and the relationship between the energy of the WSN node and the tracking performance is also disclosed.     

Integrated guidance and control strategy for homing of unmanned underwater vehicles

This paper presents a novel integrated guidance and control strategy for homing of unmanned underwater vehicles (UUVs) in 5-degree-of-freedom (DOF), where the vehicles are assumed to be underactuated at high speed and required to move towards the final docking path. During the initial homing stage, the guidance system is first designed by geometrical analysis method to generate a feasible reference trajectory. Then, in the backstepping framework, the proposed trajectory tracking controller can achieve all the tracking errors in the closed-loop system convergence to a small neighbourhood of zero. It means that the vehicle's dynamics are consistent with the reference trajectory derived in the previous step. To demonstrate the effectiveness of the proposed guidance and control strategy, the complete stability analysis used Lyapunov's method is given in the paper, and simulation results of all initial conditions are presented and discussed.     

基于遗传禁忌的数据库多连接查询优化算法

针对数据库多连接查询优化问题,提出一种基于遗传禁忌算法的数据库多连接查询优化策略。把遗传算法作为查询优化的主框架,禁忌搜索作为遗传算法的变异算子,增加种群多样性,克服遗传算法收敛慢、局部搜索能力差等缺陷。仿真结果表明,遗传禁忌算法加快了求解数据库多连接查询优化问题的速度,而且提高了查询优化效率,得到较满意的查询优化结果。     

Optimization-based adaptive neural sliding mode control for nonlinear systems with fast and accurate response under state and input constraints

The high-performance control requires the system to be stable, fast and accurate simultaneously. However, various systems (e.g., motors, industrial robots) generally face technical challenges such as nonlinearities, uncertainties, external disturbances and physical constraints, which make it difficult to reach the hardware potential of the systems to track the desired trajectories when satisfying the high-performance control requirements. Therefore, take a two-order nonlinear system for example, an optimization-based adaptive neural sliding mode control based on a two-loop control structure is proposed in this paper, where the outer and inner loops are designed separately to achieve different control requirements. Namely, the outer loop is designed as a model predictive control (MPC)-based optimization problem, which can optimize the desired trajectories to meet the state and input constraints, and maximize the converging speed of transient response as fast as possible, and the inner loop is designed with a recurrent neural network (RNN)-based adaptive neural sliding mode controller, which can guarantee the tracking of the replanned desired trajectories from outer loop as accurate as possible. The stability of the system is guaranteed by Lyapunov theorem, the optimal tracking performance is achieved under nonlinearities, uncertainties, external disturbances and physical constraints, and comparative simulation with a motor system is carried out to verify the effectiveness and superiority of the proposed approach.     

Iterative learning control for boundary tracking of uncertain nonlinear wave equations

This work presents a framework of iterative learning control (ILC) design for a class of nonlinear wave equations. The main contribution lies in that it is the first time to extend the idea of well-established ILC for lumped parameter systems to boundary tracking control of nonlinear hyperbolic distributed parameter systems (DPSs). By fully utilizing the system repetitiveness, the proposed control algorithm is capable of dealing with time-space-varying and even state-dependent uncertainties. The convergence and robustness of the proposed ILC scheme are analyzed rigorously via the contraction mapping methodology and differential/integral constraints without any system dynamics simplification or discretization. In the end, two examples are provided to show the efficacy of the proposed control scheme.