Suboptimal Control Algorithm Research Articles

A Suboptimal Economic Model Predictive Control Algorithm for Large and Infrequent Disturbances

We present a suboptimal economic model predictive control (MPC) algorithm that combines the strengths of two common suboptimal MPC approaches, one based on a warm start and one based on an optimality gap. This algorithm is specifically designed to address a class of large and infrequent disturbances that are relevant when considering discrete actuators and production scheduling in control problems. We establish that this algorithm provides the same nominal performance guarantee as optimal economic MPC and is inherently robust, in an economic context, to large and infrequent disturbances. This inherent robustness guarantee is not attained by either individual algorithm. We conclude with a small production scheduling example to demonstrate the benefits of the proposed algorithm for a practical application.

A New Adaptive Suboptimal Controller for a Class of Linear Discrete-Time Systems with Unknown Bounded Disturbances

This paper deals with adaptive suboptimal control of linear discrete-time, time-invariant, minimum phase, scalar systems in the presence of arbitrary bounded unmeasurable disturbances whose upper and lower bounds are a priori unknown. The distinguishing feature of the systems to be controlled is that there is no information concerning a priori knowledge of a bounded set to which the unknown parameters of these systems belong. Novelty of this paper is that, instead of unknown a priori membership set of parameters, the peculiar a posteriori membership sets are designed via the use of the measured signals. The adaptive suboptimal control algorithm utilizing this approach is proposed. The properties of the adaptive controller including the convergence of the adaptation procedure and also the ultimate boundedness of system's signals are established. To demonstrate an efficiency of this controller and support the theoretical study, simulation results are presented.

Dimension reduction based adaptive dynamic programming for optimal control of discrete-time nonlinear control-affine systems

Dynamic programming based methods have been widely used in solving discrete-time nonlinear constrained optimal control problems. However, applying these methods in real-time is challenging because a large amount of memory is needed and the associated computational cost is high. Here, a search space dimension reduction strategy is proposed for a class of nonlinear discrete-time systems that are control-affine and invertible. Specifically, a bio-inspired motion rule is combined with inverse dynamics to reduce the value iteration search space to one dimension. The corresponding suboptimal control algorithm is developed and its optimality is analysed. An adaptation rule is developed to estimate uncertainties and improve the base policy. The closed-loop system is proven to be asymptotically stable. The advantages of the algorithm including much smaller computational cost and significantly reduced memory usage are demonstrated with two simulation examples.

An efficient MPC algorithm for switched systems with minimum dwell time constraints

This paper presents an efficient suboptimal model predictive control (MPC) algorithm for nonlinear switched systems subject to minimum dwell time constraints (MTC). While MTC are required for most physical systems due to stability, power and mechanical restrictions, MPC optimization problems with MTC are challenging to solve. To efficiently solve such problems, the on-line MPC optimization problem is decomposed into a sequence of simpler problems, which include two nonlinear programs (NLP) and a rounding step, as typically done in mixed-integer optimal control (MIOC). Unlike the classical approach that embeds MTC in a mixed-integer linear program (MILP) with combinatorial constraints in the rounding step, our proposal is to embed the MTC in one of the NLPs using move blocking. Such a formulation can speedup on-line computations by employing recent move blocking algorithms for NLP problems and by using a simple sum-up-rounding (SUR) method for the rounding step. An explicit upper bound of the integer approximation error for the rounding step is given. In addition, a combined shrinking and receding horizon strategy is developed to satisfy closed-loop MTC. Recursive feasibility is proven using a l-step control invariant (l-CI) set, where l is the minimum dwell time step length. An algorithm to compute l-CI sets for switched linear systems off-line is also presented. Numerical studies show significant speed-up and comparable control performance of the proposed MPC algorithm against the classical approach, though at the cost of significant solution quality degradation especially when the MTC are large.

Hybrid Quasi-Optimal PID-SDRE Quadrotor Control

In the paper, a new cascade control system for an autonomous flight of an unmanned aerial vehicle (UAV) based on Proportional–Integral–Derivative (PID) and finite-time State-Dependent Riccati Equation (SDRE) control is proposed. The PID and SDRE controllers are used in a hybrid control system for precise control and stabilization, which is necessary to increase the drone’s flight stability and maneuver precision. The hybrid PID-SDRE control system proposed for the quadrotor model is quasi-optimal, since the suboptimal control algorithm for the UAV stabilization is used. The combination of the advantages of PID and SDRE control gives a significant improvement in the quality of control while maintaining the simplicity of the control system. Furthermore, the use of the suboptimal control technique provides the UAV attitude tracking in finite time. These remarks are drawn from a series of simulation tests conducted for the drone model.

Flutter control of a streamlined box girder with active flaps

Flutter control is necessary in the design of a long-span bridge. With the help of active flaps, flutter control can suppress flutter vibration and increase aerodynamic stability. This study aims to build a theoretical framework for active flutter control using a system consisting of a streamlined box girder with adjacently mounted active flaps (noted as a “deck–flap system”). An adaptive expression was proposed for the system’s self-excited forces, and an identification method was established for obtaining the system flutter derivatives in consideration of the bluff characteristics of the bridge deck and the aerodynamic interactions between the bridge girder and flaps. Then, the suboptimal control algorithm was implemented into the deck–flap system to simultaneously stabilize the divergent oscillation at the designed wind speed. Based on the proposed approach, numerical simulations were conducted to investigate the system flutter derivatives and the effectiveness of the control law. A comparison between the critical speeds of the two-dimensional flutter analysis and a fluid–structure interaction simulation showed a satisfactory performance from the theoretical model and the reliability of the identification method. The vibrations of the deck–flap system were successfully suppressed by the controlled motions of the active flaps under the application of the suboptimal control algorithm. This study provides a reliable framework for conducting an analysis of active control for bridge flutter and for significantly increasing the flutter stability of a deck–flap system.

Solving predictive control problem of fast‐varying multivariable systems by incorporating unknown active dynamics generated by real‐time adaptive learning machine

AbstractNot only adaptive predictive control of switched systems is a computationally intensive procedure, it also involves various challenges in addressing the problems of robust stabilization and precise tracking. This study proposes new strategies to deal with the aforementioned issues (namely safe and precise control alongside with reduction of computational burden). The first contribution of this work is reduction of conservatism for described class of systems. Control of switched systems with undetectable switching signals is often conducted in worst case switching configuration to ensure robustness, which potentially results in conservative design. The issue of conservativeness is intensified in multi input‐multi output (MIMO) dynamical systems due to increased dimensions. However, attaining a robust control scheme for all switching configurations while ensuring precise response is inherently paradoxical. To overcome this issue, this study proposes a new dual‐mode algorithm where control modes corresponding to safety and precision are activated at appropriate stages of system response. This is conducted based on incorporation of an adaptive fuzzy‐wavelet neural network identification scheme in predictive control of MIMO switched systems. However, as convergence of the adaptive algorithm to actual system is attained after a finite period of time, a safe‐mode control algorithm is proposed to maintain quality of transient response in convergence period. In other words, the proposed algorithm operates in safe and precise control modes to ensure robust stability in the convergence period and non‐conservative design in steady‐state. Second major contribution of the work is reduction of calculation burden based on incorporation of a suboptimal control algorithm. To this end, we propose a predictive control scheme based on a suboptimal gradient‐descent based controller, calculating feasible stabilizing inputs instead of optimal inputs. Effects of dynamical variations are incorporated in the model predictive control framework for increased compatibility with high‐speed switching dynamics. Then, based on incorporation of dual‐mode algorithm, precise steady‐state performance is attained while preventing notable perturbations in dynamical discontinuities at switching.

Synthesis of the suboptimal control algorithm for electroplating processes under conditions of uncertainty in the range of processed products

The paper discusses the main difficulties in finding the optimal control for obtaining high-quality electroplating in a rapidly changing product range. A suboptimal control search algorithm is proposed for solving this problem. This algorithm is reduced to finding the geometrically closest product to the existing ones, for which the optimal solution in the control matrix is known. The results of the suboptimal control search algorithm are given on the example of the zinc coating of a complex shaped product. Recommendations are given to improve the performance of the algorithm and the quality of the found suboptimal control.

Cross Layer Power Control and User Pairing for DL Multi-antenna NOMA

In a previous study, Kim et al. proposed a suboptimal user pairing and optimal power control algorithm for maximizing sum capacity in downlink multi-antenna non-orthogonal multiple access (NOMA) systems. First, Kim et al. calculate the correlation between all users. If the channel correlation is greater than the threshold, the user’s channel gain difference is stored in the channel gain-difference set. Then, the first and second large channel gain-differences of the user pairs are selected from the set. Based on the user pairing of Kim et al. in the physical layer, we propose novel iterative user substitution algorithm where a user is substituted if the peak signal-to-noise ratio (PSNR), the video quality, in the application layer increases after substitution. And we propose an optimal power control that minimizes the sum video distortion to maximize PSNR in the application layer. The numerical results show that the proposed cross layer optimal power control and user substitution outperforms Kim et al. by 1.4 dB in PSNR and only 1 dB away from exhaustive upper bound, when SNR = 15 dB and the number of users is 16.

Design and Analysis of an Hourglass-Type Electromagnetic Vibration Isolator

In order to maintain a good isolation performance of the isolator under low amplitude disturbance. the design method of an hourglass-type electromagnetic isolator with high electromechanical coupling performance is proposed in this paper. Combining a suboptimal Bang-bang control algorithm, the theoretical modeling and performance simulation of the isolator are also completed. The results show that the displacement amplitude at the resonance peak can be decreased by 62.64% when the maximum active force is 1.0 N under the excitation of sinusoidal displacement, and the control effect becomes better with the increase of maximum active force. Also, the root of mean square(RMS) values of output displacement can be decreased by 49.12% and 69.29% when the maximum active forces are 0.5 N and 1.0 N under the random excitation, respectively. The presented electromagnetic isolator has good vibration isolation effect under the active closed-loop control. Compared with the traditional electromagnetic isolator, the isolator has the advantages of not needing additional spring and small control current.

Application of the tuning algorithm with the least squares approximation to the suboptimal control algorithm for integrating objects

The problem of PID and PI-algorithms tuning by means of the approximation by the least square method of the frequency response of a linear algorithm to the sub-optimal algorithm is considered. The advantage of the method is that the parameter values are obtained through one cycle of calculation. Recommendations how to choose the parameters of the least square method taking into consideration the plant dynamics are given. The parameters mentioned are the time constant of the filter, the approximation frequency range and the correction coefficient for the time delay parameter. The problem is considered for integrating plants for some practical cases (the level control system in a boiler drum). The transfer function of the suboptimal algorithm is determined relating to the disturbance that acts in the point of the control impact input, it is typical for thermal plants. In the recommendations it is taken into consideration that the overregulation for the transient process when the setpoint is changed is also limited. In order to compare the results the systems under consideration are also calculated by the classical method with the limited frequency oscillation index. The results given in the paper can be used by specialists dealing with tuning systems with the integrating plants.

Near-optimal continuous control for spacecraft collision avoidance maneuvers via generating functions

This paper presents a suboptimal continuous control algorithm that would enable an active spacecraft to avoid collision with inactive space objects. To prevent collision, a penalty function whose value soars as a spacecraft is about to collide with other objects is inserted into the cost functional of an optimal control problem. Then, a two-point boundary value problem for a Hamiltonian system is constructed, and is solved with the generating functions. This algorithm can be coded step-by-step to obtain suboptimal feedback continuous control laws as truncated power series with no initial guess or iteration. This advantage over direct optimizations, however, requires moderate efforts to develop higher-order generating functions and update the penalty function parameters heuristically. In the illustrative examples, the above process allows an active satellite to smoothly circumvent other space objects or forbidden regions. The overall process is also useful for obtaining an appropriate initial guess for the direct optimization approaches in case of numerically sensitive problems because of the definiteness in its solution procedure.

Suboptimal LQR-based spacecraft full motion control: Theory and experimentation

This work introduces a real time suboptimal control algorithm for six-degree-of-freedom spacecraft maneuvering based on a State-Dependent-Algebraic-Riccati-Equation (SDARE) approach and real-time linearization of the equations of motion. The control strategy is sub-optimal since the gains of the linear quadratic regulator (LQR) are re-computed at each sample time. The cost function of the proposed controller has been compared with the one obtained via a general purpose optimal control software, showing, on average, an increase in control effort of approximately 15%, compensated by real-time implementability. Lastly, the paper presents experimental tests on a hardware-in-the-loop six-degree-of-freedom spacecraft simulator, designed for testing new guidance, navigation, and control algorithms for nano-satellites in a one-g laboratory environment. The tests show the real-time feasibility of the proposed approach.

A Cross-Layer QoS-Aware Communication Framework in Cognitive Radio Sensor Networks for Smart Grid Applications

Electromagnetic interference, equipment noise, multi-path effects and obstructions in harsh smart grid environments make the quality-of-service (QoS) communication a challenging task for WSN-based smart grid applications. To address these challenges, a cognitive communication based cross-layer framework has been proposed. The proposed framework exploits the emerging cognitive radio technology to mitigate the noisy and congested spectrum bands, yielding reliable and high capacity links for wireless communication in smart grids. To meet the QoS requirements of diverse smart grid applications, it differentiates the traffic flows into different priority classes according to their QoS needs and maintains three dimensional service queues attributing delay, bandwidth and reliability of data. The problem is formulated as a Lyapunov drift optimization with the objective of maximizing the weighted service of the traffic flows belonging to different classes. A suboptimal distributed control algorithm (DCA) is presented to efficiently support QoS through channel control, flow control, scheduling and routing decisions. In particular, the contributions of this paper are three folds; employing dynamic spectrum access to mitigate with the channel impairments, defining multi-attribute priority classes and designing a distributed control algorithm for data delivery that maximizes the network utility under QoS constraints. Performance evaluations in ns-2 reveal that the proposed framework achieves required QoS communication in smart grid.

A cross-layer resource allocation scheme for spatial multiplexing-based MIMO-OFDMA systems

We investigate the resource allocation problem for the downlink of a multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) system. The sum rate maximization itself cannot cope with fairness among users. Hence, we address this problem in the context of the utility-based resource allocation presented in earlier papers. This resource allocation method allows to enhance the efficiency and guarantee fairness among users by exploiting multiuser diversity, frequency diversity, as well as time diversity. In this paper, we treat the overall utility as the quality of service indicator and design utility functions with respect to the average transmission rate in order to simultaneously provide two services, real-time and best-effort. Since the optimal solutions are extremely computationally complex to obtain, we propose a suboptimal joint subchannel and power control algorithm that converges very fast and simplifies the MIMO resource allocation problem into a single-input single-output resource allocation problem. Simulation results indicate that using the proposed method achieves near-optimum solutions, and the available resources are distributed more fairly among users.

SUBOPTIMUM NONLINEAR CONTROL BY OPERATION SPEED CRITERION BASED ON BELLMAN-LYAPUNOV METHOD

A general-theoretical task of suboptimal nonlinear control algorithm synthesis is discussed. As an example, a two-mass electromechanical control system of a crane moving mechanism is examined taking into account load oscillations damping. The task is solved on the basis of Bellman–Lyapunov method using the concept of «invariant immersion» by operation speed criterion. The dynamics of a closed-loop system with a synthesized suboptimal regulator is investigated.

A New Congestion Control Algorithm of CDMA Systems

A new congestion control algorithm of code division multiple access (CDMA) is developed to reduce the cost of system. Firstly,the paper defines the utility function of resource throughout,and then set up the mathematics model according to the wireless resource characteristic. In the approach only the non-linear compensating term, solution of a sequence of adjoint vector differential equations, is required iteration. By taking the finite iteration of non-linear compensating term of optimal solution sequence, a suboptimal congestion control algorithm of CDMA can be obtained. It is proved by analysis in theory and system level simulation that the congestion control algorithm can enlarge system throughput while controlling system load.

Feedback Dual Controller Design and Its Application to Monocular Vision-Based Docking

A novel stochastic feedback control approach, which is capable of considering the presence of uncertainty during the controller design phase, is developed and applied to the automatic docking problem for an unmanned vehicle with a monocular vision sensor. A typical procedure for linear stochastic control employs a two-step approach that separates estimation and control: estimate the system state using noise corrupted measurements, and control the system based on the estimated state. However, for nonlinear stochastic control systems and adaptive control systems with uncertain parameters, control and estimation are often not separable because control inputs can affect not only the system state but also the quality of the state estimation. Dynamic programming and search-based methods are general solution techniques for solving these types of control problems, however, those solution techniques are often infeasible for real-time applications due to the huge computational requirements even for small problems. In this paper, a new systematic, suboptimal control algorithm is presented, which can be implemented as an online feedback controller for a stochastic control problem of moderate dimension. For an application example, automated docking of a nonholonomic vehicle with a monocular vision sensor is considered. The results from a series of numerical simulations and experimental tests are presented.

Suboptimal Hybrid Model Predictive Control: Application to Sewer Networks

This paper presents an application of the suboptimal hybrid model predictive control (HMPC) algorithm previously proposed by the authors to large scale sewer networks. HMPC relies on the on-line solution of mixed integer programs (MIP) that are known to be NP-complete and whose worst case complexity scales exponentially with problem size. Modern MIP solvers are on the other hand highly efficient at taking advantage of problem structure and usually achieve average optimization times that are much better than the worst case predicts. But as the MIP constraints depend on the current state of the plant, complexity can vary considerably and unpredictable behavior can occur. To circumvent unpredictability and to be able to enforce hard real-time computation constraints, the number of feasible nodes in the MIP problem is limited online by adding constraints to the number of possible mode sequences over the prediction horizon. It is shown that in realistic scenarios concerning control of large scale sewer networks, depending on the value of parameters related to the mode sequence constraints (MSC), drastic reductions can be achieved in optimization time. Practical issues of the approach are also addressed.

Microvibration control of coupled high tech equipment-building systems in vertical direction

Vertical ground motion induced by a moving train is one of the major sources of environmental loads that affect the normal operation of sensitive equipment installed in a high tech building nearby the railway. This paper investigates the microvibration level of a high tech building subject to nearby train-induced vertical ground motion and its mitigation using a hybrid control platform for sensitive equipment. The hybrid platform is an elastic body mounted on the building floor through a series of passive mounts and controlled by hydraulic actuators with a sub-optimal control algorithm. The finite element model and the governing equations of motion of the coupled platform-building system are established in the absolute coordinate to facilitate the feedback control and performance evaluation of the platform. The time histories of vertical ground motion are generated from the ground motion spectra that are the functions of track, train, and soil parameters. Numerical simulation and parametric studies are conducted on a typical three-story high tech building. The results show that the use of hybrid control platform can effectively reduce vertical microvibration of a batch of high tech equipment to the level satisfying the most stringent microscale velocity requirement specified in the BBN criteria. The hybrid control platform is superior to the passive platform because of its higher performance and robustness.