Suboptimal Control Scheme Research Articles

Dynamic event-triggered finite-horizon robust suboptimal control of multi-player systems with input disturbances

This paper presents an adaptive dynamic event-triggered robust finite-horizon suboptimal control scheme for multi-player nonzero-sum game of nonlinear systems with input disturbances based on dynamic programming (ADP) and integral sliding mode (ISM) control techniques. Firstly, dynamic event-triggered adaptive ISM controllers are designed to handle input disturbances that can force the system state to remain on the sliding manifold and relax the known upper bounds condition of input disturbances. Corresponding event-triggered condition is employed for ISM controller of each player to reduce the update frequency. Then, utilizing the obtained ISM dynamics, we employ ADP-based single critic neural networks to approximate the time-varying solution of the Hamilton–Jacobi equations. Thus, the event-triggered finite-horizon suboptimal controllers can be obtained, and corresponding state-based dynamic event-triggered condition is designed to improve the resource utilization. The stability property of the closed-loop system is demonstrated through the Lyapunov technique. Finally, the effectiveness of the proposed control scheme is confirmed through two simulation examples.

Dynamics analysis and chatter control of a polishing and milling nonideal flexible manipulator

Some robots are designed to be lightweight and flexible, enabling them to access small and challenging paths in various applications. These features enable robots to collaborate with humans in performing specific production tasks. However,the movement of the flexible manipulator can become self-excited when handling a cutting tool on a workpiece, which can lead to a control problem. This article presents a control solution for lightweight robotic manipulators with rotating tools, such as polishing and milling, using smart actuators. The control discretization method is also introduced to facilitate integration into digital controllers. The paper starts by describing the governing equations of the non-ideal flexible manipulator for polishing and milling and analysing its dynamic behavior. Subsequently, models for the controllers of the DC motor-only actuators and the hybrid (shape memory alloy and DC motors) actuators were formulated using shape memory alloy and a suboptimal control scheme known as the discrete state-dependent Riccati equation. The coupled system was analysed dynamically, and it was observed that it exhibits chaotic behavior. The results suggest that incorporating smart actuators into the motor group of the system could decrease the positioning error of the manipulator and significantly reduce the oscillation of the robot’s end-effector.

Relative E/I vector-based optimal and suboptimal control for continuous low thrust formation reconfiguration in circular orbits

This paper addresses the fuel-optimal satellite formation reconfiguration problem with continuous low-thrust control. Based on the relative eccentricity and inclination (E/I) theory, a comprehensive approach to optimal continuous low-thrust reconfiguration in circular or near-circular orbits is proposed. By analyzing the feasible fuel cost lower bound, the reconfiguration scenarios are categorized into four types, and the corresponding optimal or suboptimal control schemes are derived. More specifically, for suboptimal continuous control schemes, the relation between user-defined variables with fuel-cost is derived, providing a clear direction for better fuel cost. Compared with previous work that gives only feasible analytical solutions or obtains optimal solutions with numerical methods, the proposed method provides an efficient approach to optimal continuous low thrust reconfiguration for feasible scenarios and adjustable sub-optimal schemes for unfeasible scenarios. The proposed framework contributes to the practical application in engineering, enabling the design and analysis of more cost-effective space missions. The analysis of fuel cost reveals that the optimal continuous low thrust reconfiguration is limited with scenarios. The overall solutions are simulated and validated in four reconfiguration scenarios.

A suboptimal control scheme based on integrated real-time nonlinear estimation-identification approach for developed flexible joint manipulators structure

As the safety of human-robot interaction is of great interest in various applications, the flexibility of machine joints becomes increasingly important. In this paper, a general model is developed for electrically driven flexible-joint robots (ED-FJR), in which the coupled phenomena of stiffness-damping and friction in the joints are modeled as nonlinear and time-varying parameters. Because the output torque of the actuator mounted on the link cannot be measured, its state variables are estimated by the suboptimal estimator. Furthermore, the unknown parameters of joint flexibility are identified by the identification algorithm based on time-varying nonlinear least-squares error (TV-NLS), which are then used in the proposed control algorithm to compensate for negative effects and errors. The state-dependent Riccati equation (SDRE) method is developed in this paper using the combined estimator-identifier approach. The novel proposed method for a 3-degree-of-freedom (3-DOF) mechanical arm with electrically driven flexible joints is implemented and validated. The obtained results show that the system's performance has improved by 83% in terms of modeling accuracy. Furthermore, when compared to other methods, the proposed algorithm reduces tracking error by 59%, making it easier to reach the target point.

Suboptimal Repointing Maneuver of a staring-mode spacecraft with one DOF for final attitude

This paper addresses the problem of suboptimal control for repointing maneuver of a staring-mode spacecraft where the optical axis is required to point to the target orientation. Different from the traditional reorientation maneuver, the angle of the spacecraft around the optical axis does not need to be controlled. First, a simple yet efficient representation for repointing error is introduced and kinematical descriptions are established correspondingly. Then, two different control algorithms are proposed for repointing control of a staring-mode spacecraft. The first one is the inverse optimal PD-like controller that drives the spacecraft to complete repointing maneuver and the optimality properties of the proposed control law are investigated by using dynamic programming theory. The other one is a control Lyapunov function (CLF) based suboptimal control scheme incorporated with the idea of equivalent control in sliding mode control theory. The switch mechanism between CLF control and sliding mode control is established where only one control switch is needed when the state reach the sliding surface. Compared with the classical CLF method, the sliding mode based CLF approach not only guarantees the optimality, but also enhances the system robustness against model uncertainties and disturbances. Finally, numerical investigations are conducted to demonstrate the utility and optimality of the proposed control algorithm.

Reaction Control System Optimization for Maneuverable Reentry Vehicles Based on Particle Swarm Optimization

This paper presents a new parametric optimization design to solve a class of reaction control system (RCS) problem with discrete switching state, flexible working time, and finite-energy control for maneuverable reentry vehicles. Based on basic particle swarm optimization (PSO) method, an exponentially decreasing inertia weight function is introduced to improve convergence performance of the PSO algorithm. Considering the PSO algorithm spends long calculation time, a suboptimal control and guidance scheme is developed for online practical design. By tuning the control parameters, we try to acquire efficacy as close as possible to that of the PSO-based solution which provides a reference. Finally, comparative simulations are conducted to verify the proposed optimization approach. The results indicate that the proposed optimization and control algorithm has good performance for such RCS of maneuverable reentry vehicles.

Neural-network-based output-feedback control with stochastic communication protocols

This paper is concerned with the neural-network-based (NN-based) output-feedback control issue for a class of nonlinear systems. For the purpose of effectively mitigating the phenomena of data congestion/collision, the stochastic communication protocols are favorably utilized to orchestrate the data transmissions, and the resultant closed-loop plant is represented by a so-called protocol-induced Markovian jump system with uncertain transition probability matrices. Taking such an uncertainty probability into account, a novel iterative adaptive dynamic programming (ADP) algorithm is developed to obtain the desired suboptimal solution with the help of auxiliary quasi-HJB equation, and the algorithm convergence is also investigated via the intensive use of the mathematical analysis. In this ADP framework, an NN-based observer with a novel adaptive tuning law is first adopted to reconstruct the system states. Then, based on the reconfigurable system, an actor–critic NN scheme with online learning is developed to realize the considered control strategy. Furthermore, in light of the Lyapunov theory, some sufficient conditions are derived to guarantee the stability of the zero equilibrium point of the closed-loop system as well as the boundedness of the estimation errors for critic and actor NN weights. Finally, a simulation example is employed to demonstrate the effectiveness of the developed suboptimal control scheme.

Optimal Energy Allocation in Multisensor Estimation Over Wireless Channels Using Energy Harvesting and Sharing

We investigate the optimal power control for multisensor estimation of correlated random Gaussian sources. A group of wireless sensors obtains local measurements and transmits them to a remote fusion center (FC), which reconstructs the measurements using the minimum mean-square error estimator. All the sensors are equipped with an energy harvesting module and a transceiver unit for wireless, directed energy sharing between neighboring sensors. The sensor batteries are of finite storage capacity and prone to energy leakage. Our aim is to find optimal power control strategies, which determine the energies used to transmit data to the FC and shared between sensors, so as to minimize the long-term average distortion over an infinite horizon. We assume centralized causal information of the harvested energies and channel gains, which are generated by independent finite-state stationary Markov chains. The optimal power control policy is derived using a stochastic predictive control formulation. We also investigate the structure of the optimal solution, a Q-learning based suboptimal power control scheme and two computationally simple and easy-to-implement heuristic policies. Extensive numerical simulations illustrate the performance of the considered policies.

Modelling minimum-time manoeuvering with global optimisation of local receding horizon control

In this paper, we explore the notion that a human driver uses a receding horizon model predictive control (MPC) scheme for minimum-time manoeuvering. However, MPC is an inherently sub-optimal control scheme because not all future information is incorporated into its finite preview horizon. In many practical applications, this sub-optimality is tolerated as the solution is sufficiently close to optimal. However, it is known that professional drivers have the ability to learn driving circuits and exploit its features to minimise their global manoeuvering time. In this paper, we will model their process with a cascaded optimisation structure. Therein, the inner-loop features a local MPC scheme tasked with finding the control inputs that achieve a blended objective of minimising time and maximising velocity in each preview horizon/distance. The outer loop of this cascaded structure computes the best set of weights for the two components of the local objectives in order to minimise the global manoeuvering time. The proposed cascaded optimisation and control approach is compared against a straight-forward fixed-cost time optimal MPC applied to minimum-time manoeuvering over two well-known race courses. The paper also includes an extended literature review and details of the computational formulation of the model approach.

Suboptimal Learning Control for Nonlinearly Parametric Time-Delay Systems Under Alignment Condition

In order to achieve perfect trajectory-tracking performance over the entire time interval at a higher convergence speed, this paper proposes a suboptimal learning control scheme for a class of nonlinearly parametric time-delay systems under alignment condition. The controller is designed by integrating the robust learning control with the suboptimal control, in which, the control Lyapunov function and Sontag formula are employed in generating a suboptimal controller for the nominal system, while robust learning control mechanism is applied to deal with nonlinearly parametric time-delay uncertainties. As the iteration number increases, the system state can follow its reference signal over the full time interval. The proposed method extends some existing results. Numerical simulations demonstrate that our suboptimal iterative learning control scheme improves the convergence performance in comparison with traditional solutions.

Drag reduction of wall bounded incompressible turbulent flow based on active dimples/pimples

The control of turbulence by dimples/pimples has drawn more and more attention. The objective of this paper is to investigate the effectiveness of the active dimples/pimples for the drag reduction in the incompressible turbulent flow. Firstly, the drag reduction by the opposition control based on active dimples/pimples at the lower wall is studied via the direct numerical simulation of the turbulent channel flow. It is found that large active dimples/pimples can not suppress the streamwise vortices significantly and thus almost no drag reduction is achieved. Small active dimples and pimples with the diameter of one fourth of the streak width can both reduce the friction drag, but pimples will induce a larger pressure drag than dimples. Then the suboptimal control scheme is examined based on small active dimples using the spanwise wall shear information only. It is shown that the friction drag decreases by about 4.5% but the total drag is only reduced by about 2.7% abated by the pressure drag. Compared with the actuation of the all-point blowing/suction or the all-point wall movement, the effectiveness of the turbulent drag reduction based on active shallow dimples is much smaller.

Suboptimal Control Scheme Design for Interior Permanent-Magnet Synchronous Motors: An SDRE-Based Approach

This paper designs a suboptimal speed controller as well as a suboptimal load torque observer based on state-dependent Riccati equation (SDRE) approach for interior permanent-magnet synchronous motor (IPMSM) servo systems. First, dynamic equations of the IPMSMs are transformed to a suitable form that makes an SDRE-based control technique applicable. Moreover, the maximum torque per ampere (MTPA) control is incorporated to improve the torque generation in the constant torque region. The asymptotic stabilities of the proposed controller and load torque observer are fully guaranteed through an extended linear quadratic regulator (LQR) theory. This proposed method is simple to implement because the SDRE solutions are approximated off-line. The proposed observer-based suboptimal control scheme can ensure faster dynamic response, smaller steady-state error, and more robust response than the LQR and proportional-integral (PI) controller under the system parameter variations and load torque disturbances. The effectiveness of the proposed control strategy is verified via experiment.

Rate Analysis of Inexact Dual First-Order Methods Application to Dual Decomposition

We propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first-order methods based on approximate gradients for which we prove sublinear rate of convergence. In particular, we provide a complete rate analysis and estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions. Moreover, we solve approximately the inner problems with a linearly convergent parallel coordinate descent algorithm. Our analysis relies on the Lipschitz property of the dual function and inexact dual gradients. Further, we combine these methods with dual decomposition and constraint tightening and apply this framework to linear model predictive control obtaining a suboptimal and feasible control scheme.

Stochastic optimal control of unknown linear networked control system in the presence of random delays and packet losses

In this paper, the stochastic optimal control of linear networked control system (NCS) with uncertain system dynamics and in the presence of network imperfections such as random delays and packet losses is derived. The proposed stochastic optimal control method uses an adaptive estimator (AE) and ideas from Q-learning to solve the infinite horizon optimal regulation of unknown NCS with time-varying system matrices. Next, a stochastic suboptimal control scheme which uses AE and Q-learning is introduced for the regulation of unknown linear time-invariant NCS that is derived using certainty equivalence property. Update laws for online tuning the unknown parameters of the AE to obtain the Q-function are derived. Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control signals converge to optimal or suboptimal control inputs. Simulation results are included to show the effectiveness of the proposed schemes. The result is an optimal control scheme that operates forward-in-time manner for unknown linear systems in contrast with standard Riccati equation-based schemes which function backward-in-time.

Power Control for Space-Time Block Coded MIMO System with Beamforming and Imperfect Channel State Information

In this paper, an optimal power control for minimizing bit error rate (BER) subject to a power constraint for space-time block coded MIMO systems with beamforming over Rayleigh fading channels under imperfect channel state information (CSI) is presented. The optimal power control procedure is developed. It is shown that the Lagrange multiplier for the constrained optimization does exist and is unique. To simplify the power control procedure, a closed-form suboptimal power control scheme is drived based on the asymptotic performance analysis of the optimal power control and Taylor's series expansion. The calculation of the suboptimal power control is straightforward with low computational complexity. Moreover, the suboptimal scheme can provide the BER performance close to that of the optimal power control and is lower than that of the existing suboptimal scheme. Simulation results show that the proposed two power control schemes can provide BER lower than that of the equal power allocation and the existing suboptimal scheme under imperfect CSI.

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

AbstractIn this paper, learning control is integrated with non‐linear optimal control to enhance control performance of a class of non‐linear systems with time‐varying parametric uncertainties. A suboptimal control strategy based on a control Lyapunov function (CLF) and Sontag's formula provides suboptimal performance as well as stability along the time horizon for the nominal part of the non‐linear dynamic system. The proposed learning mechanism learns the unknown time‐varying parametric uncertainties so as to eliminate uncertain effects. System information both in time horizon and learning repetition horizon are incorporated in a composite energy function (CEF). The proposed control scheme achieves asymptotic convergence along the learning repetition horizon and boundedness and pointwise convergence of the tracking error (perfect tracking performance) along the time horizon. Copyright © 2001 John Wiley & Sons, Ltd.

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

A suboptimal learning control scheme for non‐linear systems with time‐varying parametric uncertainties

Grinding operation optimization of the CODELCO-Andina concentrator plant

This paper presents results following the application of a sub-optimal control scheme, both through simulation and in situ, from the operation of Section C of the CODELCO-Andina copper concentrator plant. The algorithm permits the determination of the necessary control action at each instant of time in order to maximize a defined plant performance index. The main objective of the algorithm is to maximize the mineral tonnage processed by the section, subject to it not exceeding a predetermined value establishes! for the operation conditions of the mills, while at the same time maintaining constant the mass fraction over 65 mesh (212 [microns]) in the overflow of the hydrocyclones, at a value within the operational requirements of the flotation stage. The performance index is defined in terms of; the percentage of pulp solids fed to the hydrocyclones of each line of ball mills, penalty functions to prevent electric power to the ball mills ,falling below the lower limit (so as not to enter the overload region), the tonnage processed in the section, and, since water is a scarce resource, a term considering the water added to each sump is also included. The scheme is first studied and adjusted in a simulator of a concentrator plant similar to that used in the industrial application. For plant implementation, a PC software program, denoted CONMOL, is developed in TurboPascal for Windows. This software allows plant applications to be carried out through a communications interface. Finally, the results of two tests performed on Section C of the CODELCO-Andina copper concentrator plant are shown where the control is applied over 3 and 5.5 hours respectively.

Time-optimal control of power systems requiring multiple switchings of series capacitors

Time-optimal control of switchable series or shunt capacitors requiring only a single switching has been proposed for damping power system swings resulting from large disturbances. This strategy is useful for a switchable series capacitor with a high compensation rating relative to the transmission system. In this paper, the general case of time-optimal control of series capacitors requiring multiple switchings is investigated. The strategy is applicable to a switchable series capacitor with a low compensation rating relative to the transmission system. It is illustrated for a single-machine infinite-bus system and an interconnected system. Suboptimal capacitor-switching control schemes are also investigated.

Mixed Strategy Global Sub-Optimal Feedback Control for Chaotic Systems

How to perform targeting of chaotic systems in a global sense is an important question. In this paper, we address this problem by introducing a mixed strategy global sub-optimal feedback control scheme. The idea is to partition the state space into 2 parts, namely, the target region and its complement. The proposed controller will take different forms depending on which partition of the state space the system is in. Simulations are also provided to illustrate the proposed scheme.