Optimal Performance Index Research Articles

Absolute Instantaneous Optimal Control Performance Index for Active Vibration Control of Structures under Seismic Excitation

In this paper, an instantaneous optimal control performance index for active control of structures under seismic excitation is analytically proposed. Absolute velocity and absolute displacement terms are implemented to the conventional state vector terms and eventually to the resulting performance index expression. The seismic response reduction effectiveness of the proposed performance index is compared with the linear quadratic regulator control (LQR). For numerical verification of the performance index, an eight‐story shear building with a fully active tendon controller system under unidirectional earthquake is considered as the first example. For a more complex model, a three‐dimensional tier building under the effect of bidirectional earthquakes is selected as second numerical example. Unidirectional near fault and bidirectional near fault earthquakes are used in the simulations. The control energy demand of each control method is also considered in the comparison. It is obtained from numerical simulations that the proposed performance index is as effective as LQR in attenuating structural vibrations. However, the resulting performance index does not require a priori knowledge of the seismic excitation like the LQR. The nonlinear Riccati matrix equation solution of the LQR is not required in the proposed performance index as well.

$H_{\infty}$ Control for Discrete-Time Markov Jump Linear Systems via Static Output Feedback

This paper addresses the problem of $H_{\infty }$ control for discrete-time Markov jump linear systems via static output feedback. The transition probabilities of Markov chain are assumed to be partly unknown. First, by utilizing the properties that the sum of each row is one in a transition probability matrix and constructing Lyapunov function, a sufficient condition is established such that the system under consideration is stochastically stable with a pre-specified $H_{\infty }$ performance index. Second, the design method of static output feedback controller is proposed to guarantee that the resultant closed-loop system is stochastically stable with the pre-specified $H_{\infty }$ performance index $\gamma $ . Since the conditions obtained for the existence of controllers are not expressed strictly in terms of linear matrix inequalities, a modified cone complementarity linearization algorithm is given to solve the static output feedback controller gains. Finally, a numerical example is presented to show the effectiveness of the theoretic results. Compared with the existing literature, the total number of matrix inequalities in the proposed method is less, and the optimal performance index obtained is smaller.

2D Fuzzy Constrained Fault-Tolerant Predictive Control of Nonlinear Batch Processes

Concerning actuator gain faults and strong system nonlinearity in batch processes, a design method of a kind of 2D fuzzy constrained model fault-tolerant predictive controller is proposed. Firstly, introduce two errors: state error and output error, after that the original system model is converted into a 2D Roesser fault model. Meanwhile, the design of iterative learning fault tolerant control under constraints has been transformed into the determination of the constrained update law. Subsequently, real-time on-line design of the fuzzy fault-tolerant update law that ensures the closed-loop system robustly asymptotic stability is presented by taking the appearance of linear matrix inequalities (LMIs) with constraint subject to the designed infinite optimization performance index and Lyapunov stability theory. Finally, taking a three-tank case as an example to compare with the 1D of the method proposed in this paper, the comparison results illustrated the 2D method of this paper has better control effects.

Fuzzy-Set Theory Based Optimal Robust Design for Position Tracking Control of Permanent Magnet Linear Motor

In this paper, we design an optimal robust control to address the problem of position tracking control for permanent magnet linear motor (PMLM). The uncertainties in PMLM system, including parameters uncertainty and external disturbance, are nonlinear and time-varying. The uncertainties are assumed to be bounded, and the bounds are described via fuzzy sets. Then, a model-based robust control in deterministic form is proposed. Furthermore, an optimal robust control for PMLM system is formulated as a fuzzy performance index optimization problem, which associated with both the fuzzy system performance and the control cost. The resulting optimal control can guarantee the uniform boundedness and uniform ultimate boundedness. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness of the optimal robust control for PMLM.

Filtering of T–S Fuzzy Systems With Nonuniform Sampling

The problem of asynchronous filtering of nonlinear systems is investigated in this paper. To facilitate analysis, a discrete-time Takagi-Sugeno fuzzy model with a fast and uniform period is introduced to approximate continuous nonlinear systems. A slow and nonuniform sampler between system and filter is proposed to overcome the contradictions between fast sampling period and limited bandwidth. The nonuniform sampling interval of sampler is subject to a Markov chain. To make full use of the partial information of sampling interval which is accessible to the filter, the asynchronous filter which is described by the hidden Markov model is introduced to reduce conservatism. By resorting to the augmentation approach and the Lyapunov functional method which depends on nonuniform sampling interval, some sufficient conditions for the existence of asynchronous filer are given to guarantee the stability and dissipativity of the augmented system. The gains of asynchronous filter are given via solving a set of linear matrix inequalities. Two examples are utilized to illustrate the validity of the developed filter design technique where the relationships between optimal dissipative performance indices and the mode synchronization rate are given.

Double‐deck optimal schedule of micro‐grid based on demand‐side response

In order to fully consume renewable energies and schedule demand-side resources more hierarchically, a double-deck optimal schedule model of micro-grid, which connects to power grids and concludes battery energy storage system (BESS), is proposed. Unlike the original peak-valley time-of-use (TOU) price, in the upper layer optimal schedule, the improved TOU price which takes account into the user's satisfaction can express the adjusted loads accurately and the resulting net loads can be treated as a link between upper and lower layer scheduling. For the reason of having no precise model of BESS, the lower model for the goal of minimising the operation cost is solved by action dependent heuristic dynamic programming algorithm that is not relying on the accurate controlled object model. This algorithm is used to obtain the most optimal performance index function and control strategy by the optimal iterative process, which is based on the back propagation neural network used for evaluating the optimal performance index. Analysis of examples and results has been presented to show the effectiveness of the proposed strategies.

A Novel Discrete-time Nonlinear Model Predictive Control Based on State Space Model

This paper proposes a novel finite dimensional discrete-time Nonlinear Model Predictive Control. This technique is based on discrete-time state-space models, Taylor series expansion for prediction and performance index optimization. Furthermore, the technique extends the concept of the Lie derivative for the discrete time case using Euler backwards method. The performance validation for the discrete-time Nonlinear Model Predictive Control uses the simulation of a single-link flexible joint robot and the inverted pendulum. Comparison of the proposed finite dimensional discrete-time Nonlinear Model Predictive Control technique with Feedback Linearization Control is also discussed. Analytical and numerical results show excellent performances for both, the single-link flexible joint and inverted pendulum controllers using the proposed discrete-time Nonlinear Model Predictive Control technique.

Adjustment of Pole Placement Algorithm Based on Vulnerability Reduction of Skewed Bridges

Skewed bridges due to the specific dynamic characteristics have shown vulnerability in recent strong earthquakes. In this study, an active control strategy is employed to optimize the seismic performance of a typical model of such structures. As the control algorithm, the pole placement method has been used, of which the key factor is selection of desired poles to achieve desired dynamic responses. A performance index (PI) was defined as a function of displacement and rotation of a bridge deck. The desired poles for the algorithm were extracted by optimizing this index. A previously presented and approved simplified model of a skewed bridge with the three degrees of freedom was selected as a typical model, and the methodology was applied on this model. The optimization of PI was carried out by a series of time-history analysis. Ten far-field ground-motion records presented in FEMA-P695 were used for this purpose. The PI was calculated for a range of damping ratio and frequency of the system, and the desired poles were selected for the optimum values of PI. The results show that the control of the model using the selected pole by this method could effectively reduce the displacement and rotation of the bridge model.

Active Control on Path Following and Lateral Stability for Truck–Trailer Combinations

Low-speed path following and high-speed lateral stability are vital performance for safety driving of truck–trailer combinations (TTCs). These two performance can be effectively improved by active trailer steering (ATS) system. This paper investigates low-speed path following and high-speed lateral stability for TTCs with ATS system. First of all, the driver model and yaw plane model of TTC are proposed to capture the optimal control performance index. Next, a method based on shift register operation is proposed to deduce the path-following off-tracking (PFOT) of TTC. Then, two controllers of path following and lateral stability are designed, respectively. Finally, numerical experiments on the directional performance of TTC are carried out under the low-speed $$90{^{\circ }}$$ intersection turn and $$360{^{\circ }}$$ roundabout maneuvre, and the high-speed single lane-change maneuvre. The numerical results demonstrate that the TTC with ATS system improves both low-speed path following and high-speed lateral stability compared with the baseline TTC without ATS system, and the designed controllers have good performance on reducing PFOT and RWA in any maneuvre conditions.

Ship Navigation System Based on Wireless Sensor

To study the application of wireless sensor in the ship dynamic positioning system, the distributed fusion function model and structure model of wireless sensor network were set up.Using the DJC model-based SVM prediction algorithm, the quadratic optimal performance index in ship dynamic positioning MPC control was solved and the optimal control thrust was obtained.According to the classic cluster routing protocol, a data fusion structure based on residual energy and dormancy scheduling mechanism was proposed. The results showed that the proposed routing protocol based on the residual energy and sleep scheduling mechanism data fusion structure was superior to the Leach protocol. It improved the real-time performance of data transmission. Thus, the network data fusion structure achieves the goal of energy balance. The energy consumption is reduced to a certain extent and the design is reasonable.

Robust guaranteed cost control for continuous-time uncertain Markov switching singular systems with mode-dependent time delays

The guaranteed cost control problem for mode-dependent time-delay Markov switching singular systems with norm-bounded uncertain parameters is discussed. Based on delay-dependent linear matrix inequalities, sufficient conditions which ensure the nominal Markov switching singular system to be regular, non-impulsive and stochastically stable are derived by quoting a mode-dependent Lyapunov functional and applying Moon’s inequality for cross terms. The sufficient conditions involve two cases. Case 1: the time delays are known; Case 2: the time delays are unknown, but the difference of the largest and the smallest time delay is known. Then, the problem is solved to design a state-feedback control law such that the closed-loop system is stochastically stable and the corresponding cost function value is not bigger than a specified upper bound for all the admissible uncertainties. Finally, optimization algorithms are given to find the optimal performance indexes.

Filtering of two-dimensional periodic Roesser systems subject to dissipativity

In this note, the problem of dissipativity-based filtering of two-dimensional (2D) periodic Roesser systems is investigated. A discrete-time periodic Roesser model extensively used in practical systems is introduced to describe 2D periodic systems. Moreover, it is assumed that the periods of the augmented system in horizontal and vertical directions are the same, which can greatly simplify stability analyses. By resorting to the periodic Lyapunov functional approach that depends on periodical property of the augmented system, less conservative results for the existence of 2D periodic filter are presented to ensure the asymptotic stability and 2D (Q1,Q2,Q3)−β-dissipativity. Particularly, the parameters of 2D periodic filter are derived with convex optimization method. Simulation results are provided to verify the effectiveness and merits of the theoretical findings. In addition, the correlation between optimal dissipative performance indices and different Lyapunov functions is revealed.

Finite-Time Non-fragile Dissipative Stabilization of Delayed Neural Networks

This article studies the finite-time non-fragile dissipativity issue of time-delayed neural networks. The main purpose of this study is to synthesize the finite-time non-fragile and dissipativity controller guaranteeing the finite-time boundedness of the resulting neural networks (NNs) with optimal dissipative performance index. By constructing appropriate Lyapunov–Krasovskii functional, combining with Jensen’s inequality and Wirtinger’s based integral inequality, a new delay-dependent finite-time boundedness of dissipativity criteria is obtained in terms of linear matrix inequalities techniques. The finite-time non-fragile state-feedback controller is designed to ensure the strict dissipativeness of the concerned NNs. In addition, these conditions are obtained with less conservative results than those in the existing approaches, which has been shown through numerical examples.

Low cognitive flexibility as a risk for heavy alcohol drinking in non-human primates.

Chronic alcohol abuse is frequently considered a habitual or inflexible behavior; however, measures of pre-existing cognitive flexibility prior to initiation of alcohol use are usually not available. This study used rhesus monkeys and an attentional set-shifting task to investigate whether pre-existing cognitive flexibility would predict increased risk for heavy alcohol drinking. As previously reported, monkeys were given 30 daily set-shifting sessions prior to alcohol access. These sessions consisted of the same sequence of eight unique visual discriminations (sets) of two objects that varied on two dimensions (shapes and colors). The ratio of errors per trials, session duration, and maximum set reached were primary dependent variables from each session and were used to compose a session performance index (PI) that ranged from a low performance PI of 31 to an optimal performance PI of 247. Here, animals underwent an alcohol induction period followed by 22 weeks of daily (22-h) self-administration sessions with free access to water and alcohol. Based on average daily alcohol intake during 22 weeks of 22-h/day access, the monkeys were categorized as non-heavy (mean=2.0±0.3g/kg/day; n=3) and heavy (mean=3.3±0.5g/kg/day; n=6) drinkers. The two groups diverged in performance on the set-shifting task across the 30 pre-alcohol sessions, and at the end of the pre-alcohol testing, the group average PI was 216±27 and 137±71 for the future non-heavy and heavy drinkers, respectively. The data show that low cognitive flexibility assessed with a set-shifting procedure was predictive of future classification as a heavy alcohol drinker. The data highlight individual differences in both cognitive flexibility and in alcohol self-administration in this population of rhesus monkeys.

Asynchronous and Resilient Filtering for Markovian Jump Neural Networks Subject to Extended Dissipativity.

The problem of asynchronous and resilient filtering for discrete-time Markov jump neural networks subject to extended dissipativity is investigated in this paper. The modes of the designed resilient filter are assumed to run asynchronously with the modes of original Markov jump neural networks, which accord well with practical applications and are described through a hidden Markov model. Due to the fluctuation of the filter parameters, a resilient filter taking into account parameter uncertainty is adopted. Being different from the norm-bound type of uncertainty which has been studied in a considerable number of the existing literatures, the interval type of uncertainty is introduced so as to describe uncertain phenomenon more accurately. By means of convex optimal method, the gains of filter are derived to guarantee the stochastic stability and extended dissipativity of the filtering error system under the wave of the filter parameters. Considering the limited computing power of MATLAB solver, a relatively simple simulation is exploited to verify the effectiveness and merits of the theoretical findings where the relationships among optimal performance index, uncertain parameter σ , and asynchronous rate are revealed.

Reduced-Order Filtering of Delayed Static Neural Networks With Markovian Jumping Parameters

The reduced-order filtering problems are investigated in this paper for static neural networks with Markovian jumping parameters and mode-dependent time-varying delays. By fully making use of integral inequalities, the designs of reduced-order and filters are discussed. The proper gain matrices of filters and the optimal performance indices are efficiently obtained by resolving corresponding convex optimization problems with the constraints of linear matrix inequalities. It is verified that the computational complexity for the reduced-order filter design is significantly reduced when compared with the full-order one. Furthermore, the nonfragile reduced-order filtering problems are also resolved in this paper. Two examples with simulation results are presented to demonstrate the feasibility and application of the established results.

Receding horizon consensus of general linear multi-agent systems with input constraints: An inverse optimality approach

This paper investigates the optimal consensus problem for general linear MASs (of semi-stable and unstable dynamics) subject to control input constraints. The optimal consensus protocols are first designed by inverse optimality approach, based on which the centralized receding horizon control (RHC)-based consensus strategies are designed and the feasibility and consensus properties of the closed-loop systems are analyzed. Utilizing the centralized one, distributed RHC-based consensus strategies are developed. We show that (1) the optimal performance indices under the inverse optimal consensus protocols are coupled with the network topologies and the system matrices of subsystems; (2) the unstable modes of subsystems impose more stringent requirements for the parameter design; (3) the designed RHC-based consensus strategies can make the control input constraints fulfilled and ensure convergent consensus and consensus for MASs with semi-stable and unstable subsystems, respectively.

Delay-Dependent Fault-Tolerant Shape Control for Stochastic Distribution Systems

A new adaptive delay-dependent fault-tolerant shape control strategy is proposed for the stochastic distribution system with time-delay, which can effectively make the output probability density function (PDF) track a given target distribution. In this framework, first, a system model based on PDF with the actuator failure is constructed. And then, adaptive delay-dependent fault-tolerant controllers, which include a normal controller and an adaptive compensation controller is designed. The normal controller can track the given output distribution with an optimized performance index when there is no actuator fault, and the adaptive compensation controller can reduce the negative effects caused by the actuator fault. Numerical simulations are used to show the effectiveness of the proposed method.

Embedded Position Control of Permanent Magnet Synchronous Motor Using Model Predictive Control

This paper presents an implementation embedded system for position control of Permanent Magnet Synchronous Motor (PMSM). The control system consists of raspberry pi 3 as a microcontroller, ASDA-A2 servo drive, and Delta Servo ECMA type. The software design includes simulation tool and Python included on Raspbian OS. Communication between Raspberry Pi 3 and ASDA-A2 drivers using the ASCII Modbus communication protocol. Raspberry Pi 3 processes the reference data and the actual reading result and calculates the resulting error. The control algorithm used in this research is Model Predictive Control (MPC). As a Linear Quadratic Regulator, MPC aims to design and generate an optimal control signal with the ability to anticipate saturation, receding horizon, future event and take control accordingly In the design of the MPC technique to adjust the speed of the PMSM to take action of reference tracking, performance index optimization is done by adjusting the value of weighting horizon N, Q and R. The simulation and implementation results showed that the PMSM can reach the stability point on each desired setpoint and result in a near-zero steady-state error.

Implications of the degree of controllability of controlled plants in the sense of LQR optimal control

ABSTRACTIn this paper, the relationship between the degree of controllability (DOC) of controlled plants and the corresponding quadratic optimal performance index in LQR control is investigated for the electro-hydraulic synchronising servo control systems and wind turbine systems, respectively. It is shown that for these two types of systems, the higher the DOC of a controlled plant is, the better the quadratic optimal performance index is. It implies that in some LQR controller designs, the measure of the DOC of a controlled plant can be used as an index for the optimisation of adjustable plant parameters, by which the plant can be controlled more effectively.