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In Off-Policy reinforcement learning (RL), the experience imbalance problem can affect learning performance. The experience imbalance problem refers to the phenomenon that the experiences obtained by the agent during the learning process are unevenly distributed in the state space, resulting in the agent's inability to accurately estimate the value of each potential state. This problem is typically caused by environments with high-dimensional state and action spaces, as well as the exploration–exploitation mechanism inherent in RL. This article proposes a balanced prioritized experience replay (BPER) algorithm based on experience rarity. First, an evaluation metric to quantify experience rarity is defined. Then, the sampling priority of each experience is calculated according to this metric. Finally, prioritized experience replay is performed according to the sampling priority. BPER increases the sampling frequency of high-rarity experiences and decreases the sampling frequency of low-rarity experiences, enabling the agent to learn more comprehensive knowledge. We evaluate BPER on a series of MuJoCo continuous control tasks. Experimental results show that BPER can effectively improve the learning performance while mitigating the impact of the experience imbalance problem. [ABSTRACT FROM AUTHOR]

Numerical weather prediction (NWP) is widely used for day-ahead solar irradiance forecast, which is essential for applications in day-ahead energy market and energy management of different scales ranging from public level to civil level. In the literature, many NWP correction methods have been proposed to obtain more accurate solar irradiance forecast. However, when facing different real-world scenarios, it is crucial to efficiently design corresponding correction schemes, which require a detailed and reliable error evaluation foundation. To solve this problem, the performance for day-ahead NWP Global Horizontal Irradiance (GHI) forecast is evaluated under different weather conditions and seasons. The statistical analysis was conducted at each time of day and each NWP GHI forecast level with both publicly available datasets and actual field dataset, aiming to explore the detailed error characteristics of NWP GHI forecasts. The results demonstrate variations in NWP GHI error across diverse weather conditions and seasons, which indicates that future NWP GHI corrections should be developed under different weather conditions and seasons. For weather conditions, NWP GHI forecasts have the lowest accuracy during overcast conditions, followed by cloudy conditions, while the highest accuracy is observed during sunny conditions. Moreover, overestimations are more likely to occur during overcast and cloudy conditions. For seasons, the accuracy of NWP GHI forecasts is generally highest during winter. Additionally, we have summarized some common error characteristics under different weather conditions and seasons. This study provides useful information for improving the accuracy and efficiency of NWP correction works and for the stable operation of power systems. [ABSTRACT FROM AUTHOR]

This article proposes a robust H∞$$ {H}_{\infty } $$ control method based on disturbance observer techniques for systems subject to mismatched uncertainties/disturbances. In the existing composite robust H∞$$ {H}_{\infty } $$ control methods with disturbance compensation, only matched uncertainties/disturbances, that is, the uncertainties/disturbances acting on the same channels as the control inputs, are feedforward compensated, while the mismatched ones are only attenuated in a conservative manner. It should be highlighted that if the mismatched uncertainties/disturbances are nonvanishing, the controller generally requires excessive control energy to suppress the effects of uncertainties/disturbances, where the control gains must be designed to ensure robust properties at the expense of sacrificing nominal tracking and/or stabilization performances. To address this problem, this article further introduces the compensation of mismatched uncertainties/disturbances into the robust H∞$$ {H}_{\infty } $$ control. Moreover, to attenuate the effects of observation errors, sufficient conditions for the asymptotic and robust stability of error systems are established. Finally, the proposed controller is applied to a DC–DC buck converter system feeding constant power load. Experimental results confirm its feasibility and efficiency. [ABSTRACT FROM AUTHOR]

Day-ahead photovoltaic (PV) power forecasting plays a crucial role in power market trading and grid dispatching. It has been empirically demonstrated in various fields that combining forecasts yields better results than using individual models. In this work, a novel adaptive ensemble framework is proposed based on multi-source data. First, incorporating prior information from physical models, three types of high-performance component models are constructed based on different types of data. Second, a multi-label classification method is utilized to select better performing models, allowing for switching between different model combinations depending on the weather conditions. Finally, a dynamic ensemble method is used to update the weights of the component forecasts based on its cumulative errors observed in the recent past. The proposed method was evaluated on a four-year PV multi-source dataset from 2019 to 2022. The forecasting skill (FS) in the test year (2022) reaches 50.61%. The results show that FS is improved by 4.75% compared to the optimal component model. Compared with other state-of-the-art methods, our method has achieved the best performance by improving FS at least 3.94%. The proposed framework in this study can be widely applied to other energy forecasting fields, such as wind/load forecasting. [ABSTRACT FROM AUTHOR]

In this study, we consider the finite time stability (FTS) and finite time contractive stability (FTCS) of the stochastic functional systems. For the framework of Lyapunov-Ruzumikhin method, the sufficient conditions of FTS and FTCS are given first. Then the theory is applied to FTS and FTCS of linear time-varying stochastic functional systems. Finally, experiments on the numerical examples have demonstrated the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

The acceptance check is a key step to decide whether an overhead transmission line can be put into use. However, for the acceptance check of towers, the manual means is still adopted mostly nowadays, which is dangerous and inefficient. The main challenges for intelligent check technique are the automatic tower segmentation and intelligent requirements of some detection items. Here, based on point clouds from lidars, some intelligent methods are proposed for tower related acceptance check items. The geometric structural changing rules for towers are found and analyzed to identify and segment towers from the scene point cloud automatically. A model‐constrained method is proposed for fine filtering of towers. With point cloud registration strategies, the tilt angle of a tower is calculated intelligently and the defect detection of a tower is conducted successfully. Experiments show that the results of the proposed methods are accurate, efficient and automatic, which have potential for real applications. [ABSTRACT FROM AUTHOR]

This paper considers an optimization problem of switched dynamical processes, which is essentially a mixed integer optimization problem. Unlike the existing optimization problem, the state-dependent switching strategy is adopted to design the switching rules. Our main contributions are as follows. Firstly, by introducing a discrete-valued function, a control vector parameterization technique, and a novel relaxation technique, the switched dynamical process optimization problem is approximated by using a more tractable nonlinear constrained parameter optimization problem. Unlike the existing works, the number of locally optimal solution does not increase due to the relaxation transformation. Next, in order to obtain a numerical solution of this parameter optimization problem, a novel penalty function approach is developed. Unlike existing penalty functions, this novel penalty function is neither quadratic nor linear, and has exponential convergence rates. Furthermore, a sensitivity analysis method is developed for investigating the effect of small perturbations in constraints and switching conditions on the objective function. Finally, a dynamic optimization problem in cancer chemotherapy process is presented to illustrate the effectiveness of the approach provided by this paper. Numerical simulation results show that the approach provided by this paper is low time-consuming, has faster convergence speed, can obtain a better objective function value than the existing methods, and is robust for the small perturbations in constraints and switching conditions. [ABSTRACT FROM AUTHOR]

This paper considers an optimization problem of nonlinear dynamical processes with discrete-valued input and continuous-time inequality constraints. This problem requires to determine an order and some instants. Since the order is a discrete variable and the constraints are complex, classical optimal control approaches cannot be used directly to solve this problem. To tackle this issue, a penalty function-based greedy diffusion search algorithm is proposed based on a novel transformation for each discrete value, a novel second-order smoothing technique, a $ l_1 $ penalty function, and a novel greedy rule. In the novel greedy rule, there exist only two parameters, which can be set in advance. Thus, unlike existing hybrid approaches, no parameters is required adjusted in the penalty function-based greedy diffusion search algorithm. Following that, the global convergence results of the proposed algorithm are established. Finally, an energy management problem in an electrical vehicle is used to illustrate the effectiveness of the proposed algorithm. The numerical simulation results show that the algorithm proposed by this paper can obtain a better solution with less time-consuming, fewer iterations, and fewer errors compared with existing methods. [ABSTRACT FROM AUTHOR]

In recent years, how to discover causality rather than correlation among climate variables and how to use causality to help in time-series tasks have received great concern. However, the high dimensionality and nonlinearity of climate variables are the main issues for causal inference based on historical large-scale climate time series. Therefore, a method based on neural Granger causality inference is proposed to study the interactions of climate variables, with focus on the variables commonly used in the energy field, especially in photovoltaics. Firstly, for each climate variable, the time-varying causality and global causality are, respectively, obtained on each time window and on the whole series by neural Granger causality inference. Secondly, the global causality is used as a feature selection map of the input variables in the prediction task. Finally, compared with some existing feature selection methods, the experiments determine that the proposed method not only reveals the appropriate causality rather than the correlation among climate variables, but also efficiently reduces the input dimensionality and improves the performance and interpretability of the predicting model. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control problem of nonlinear systems with mixed control variables and probability constraints. To obtain a numerical solution of this optimal control problem, our target is to formulate this problem as a constrained nonlinear parameter optimization problem (CNPOP), which can be solved by using any gradient-based numerical computation method. Firstly, some binary functions are introduced for each value of the discrete-valued control variable (DCV). Following that, we relax these binary functions and impose a penalty term on the relaxation such that the solution of the resulting relaxed problem (RP) can converge to the solution of the original problem as the penalty parameter increases. Secondly, we introduce a simple initial transformation for the probability constraints. Following that, an adaptive sample approximation method (ASAM) and a novel smooth approximation technique (NSAT) are adopted to formulate the probability constraints as some deterministic constraints. Thirdly, a control parameterization approach (CPA) is used to transform the deterministic problem (i.e., an infinite dimensional problem) into a finite dimensional CNPOP. Fourthly, in order to combine the advantages of limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms and differential evolution (DE) algorithms, a L-BFGS-based DE (L-BFGS-DE) algorithm is proposed for solving the resulting approximation problem based on an improvied L-BFGS (IL-BFGS) method and an improved DE (IDE) algorithm. Following that, we establish the convergence result of the L-BFGS-DE algorithm. The L-BFGS-DE algorithm consists of two stages. The objectives of the first and second stages are to obtain a probable position of the global solution and to accelerate the convergence rate, respectively. In the IL-BFGS method, we propose a novel updating rule (NUR), which uses not only the gradient information of the objective function but also the value of the objective function. This will improved the performance of the IL-BFGS method. In the IDE algorithm, a novel adaptive parameter adjustment (NAPA) method, a novel population size decrease (NPSD) strategy, and an improved mutation (IM) scheme are proposed to improve its performance. Finally, an anti-cancer drug therapy problem (ADTP) is further extended to illustrate the effectiveness of the L-BFGS-DE algorithm by taking into account some probability constraints. Numerical results show that the L-BFGS-DE algorithm has good performance and can obtain a stable and robust performance when considering the small noise perturbations in initial state. [ABSTRACT FROM AUTHOR]

Practical industrial process is usually a dynamic process including uncertainty. Stochastic constraints can be used for industrial process modeling, when system sate and/or control input constraints cannot be strictly satisfied. Thus, optimal control of nonlinear systems with stochastic constraints can be available to address practical industrial process problems with integer‐valued control inputs. In general, obtaining an analytical solution of this optimal control problem is very difficult due to the discrete nature of the control inputs and the complexity of stochastic constraints. To obtain a numerical solution, this problem is formulated as a finite dimensional static constrained optimization problem. First, the integer‐valued control input is relaxed into a continuous‐valued control input by imposing a penalty term on the objective function. Convergence results show that the relaxed solution obtained is an integer solution as long as the penalty parameter is sufficiently large. In addition, it should be noted that no any constraint is introduced in the novel relaxation technique, which can effectively avoid introducing any extra extreme point for the original optimal control problem. Next, a novel smooth approximation function is used to construct a subset of feasible region for this optimal control problem. It is proved that the smooth approximation can converge uniformly to the stochastic constraints as the adjusting parameter reduces. Following that, a numerical computation method is proposed for solving the original optimal control problem. Finally, in order to illustrate the effectiveness of the proposed method, an electric vehicle energy management problem is extended by considering some stochastic constraints. The numerical results show that the proposed method is less conservative compared with the existing typical approaches and can obtain a stable and robust performance when considering the initial condition small perturbations. [ABSTRACT FROM AUTHOR]

In this article, an optimal timing fault tolerant control strategy is addressed for switched stochastic systems with unknown drift fault for each switching point. The proposed controllers in existing optimal timing control schemes are not directly aimed at the switched drift fault system, which affects the optimal control performance. A cost functional with system state information and fault variable is constructed. By solving the optimal switching time criterion, the switched stochastic system can accommodate switching drift fault. The variational technique is presented for the proposed cost function in deriving the gradient formula. Then, the optimal fault tolerant switching time is calculated by combining the Armijo step-size gradient descent algorithm. Finally, the effectiveness of the proposed controller design scheme is proved by the safe trajectory planning for a four wheel drive mobile robot and numerical example. [ABSTRACT FROM AUTHOR]

Irradiance prediction is a vital task in the renewable energy field. Its aim is to forecast the irradiance or power of a photovoltaic plant and thus provide a reference for stabilizing the power grid. In the real scenarios, missing data can significantly reduce the accuracy of the prediction. Meanwhile, due to the unawareness of the distribution of datasets, it is difficult to choose a suitable imputation method before modeling. Also, different imputation methods do not have the same good effects on different datasets. In this article, a recurrent neural network with an adaptive neural imputation module is proposed for forecasting direct solar irradiance using missing data. The model predicts future 4‐h irradiance based on the missing historical climate and irradiance data without imputing the data in pre‐processing stage. The proposed model is tested on the open access datasets, with missing values generated randomly in all input series. The model performance is compared under various missing rates and different input factors with other imputation methods. The results demonstrate that the proposed methods outperform other methods under different evaluation metrics. Furthermore, the authors integrate the model with the attention mechanism and find it has better performance at high irradiance. [ABSTRACT FROM AUTHOR]

This paper considers an optimal scheduling problem of maintenance and production for a machine. Firstly, the problem is formulated as a stochastic switched impulsive optimal control problem. However, there exists the stochastic disturbance in this model. Thus, it is difficult to solve the problem by conventional optimisation techniques. To overcome this difficulty, the stochastic switched impulsive optimal control problem is transformed into a deterministic switched impulsive optimal control problem with continuous state inequality constraints. Then, by combining a time-scaling transformation, a second-order smoothing technique and a penalty function method, an improved Newton algorithm is developed for solving this problem. Convergence results indicate that the algorithm is globally convergent with quadratic rate. Finally, two numerical examples are provided to illustrate the effectiveness of the developed algorithm. [ABSTRACT FROM PUBLISHER]

This paper considers an event‐triggered adaptive fixed‐time output feedback fault tolerant control problem for a class of uncertain planar nonlinear systems, in which the actuator has an unknown drift fault and the loss of effectiveness fault. Firstly, by using the adaptive backstepping technique and event‐triggered theory, a constructive event‐triggered adaptive fixed‐time state feedback controller is presented under a generalized Lipschitz continuous condition. Secondly, for the unmeasured state, a continuous fixed‐time observer is constructed. It is shown that the global practically fixed‐time stability of the closed‐loop systems is ensured by the bilimit homogeneity technique and Lyapunov theory analysis. Moreover, the system is demonstrated by contradiction to be nonzeno. Finally, the fan speed control system is constructed to demonstrate the validity of the proposed strategy and the application of the general systems. [ABSTRACT FROM AUTHOR]

Industrial processes often include shifting operating phases and dynamics, and system uncertainty. Industrial time series data may obey different distributions because of the time-varying characteristic. Therefore, a single global model cannot describe the local characteristics of multiple distributions. In this work, a hybrid GMM-IGPR model is proposed to solve this kind of time series prediction problem by using an improved Gaussian process regression (GPR) based on Gaussian mixture model (GMM) and a variant of the basic particles swarm optimization (PSO). In a first treatment to the time series, different distributions of the original dataset are characterized by adopting the GMM as a cluster method. Then, multiple localized GPR models are built to characterize the different properties between inputs and output within various clusters. In order to optimize the proposed algorithms, this paper utilizes the DEPSO which introduces differential evolution (DE) operator into the basic PSO algorithm to estimate hyperparameters of the GPR model, instead of using the traditional conjugate gradient (CG) method. Lastly, the Bayesian inference strategy is used to estimate the posterior probabilities of the test data with respect to different clusters. The various localized GPR models are integrated through these posterior probabilities as the weightings so that a global predictive model is developed for the final prediction. The effectiveness of the proposed algorithm is verified by means of a numerical example and a real industrial winding process. Statistical tests of experimental results compared with other popular prediction models demonstrate the good performance of the proposed model. [ABSTRACT FROM AUTHOR]

As a key component of human–computer intelligent interaction and many real-world applications, the real-time property of facial expression recognition is especially important. However, the recognition result of conventional video-based approaches can not be given until the entire video is finished. In this letter, we deal with early expression detection, which aims to identify the expression as early as possible before its ending. This is a relatively new and challenging problem. Max-margin early event detector (MMED) is a well-known framework, which can make early detection. However, the linearity restricts its applications. We thus introduce kernel learning to model the nonlinear structure of complex data distribution. Moreover, the model is further reformulated in an online setting to address the streaming videos. The high retraining cost and large memory requirement of MMED are thus significantly reduced. In addition, we employ AlexNet architecture to make further comparison with mid-level features. Experiments on two popular video-based expression datasets demonstrate both the effectiveness and efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The accurate estimation of direct normal irradiance (DNI) under clear sky conditions plays an important role in the concentrated solar thermal plant. A hybrid model with adjustable inputs is proposed to calculate the clear-sky DNI, including a base clear-sky model and an error-correction model. The base clear-sky model is able to estimate the clear-sky DNI at any place with only the local date and location information, and the error-correction model serves as a supplementary to improve the calculating accuracy with available meteorological data. The error-correction model effectively integrates a linear part and a nonlinear part, and its inputs are adjustable according to the available meteorological observations. Several experiments have been conducted to evaluate the performance of the proposed model with data from three observation stations provided by the National Renewable Energy Laboratory open database. The results show that the hybrid model is able to provide great improvement over the base clear-sky model with 28%–70% on normalized root mean square error, and it also performs better than those using a linear or nonlinear error correction model. It is concluded that the performance of the hybrid model is comparable with other published methods in calculating the clear-sky DNI with concrete statistics. [ABSTRACT FROM AUTHOR]

This paper considers the optimal control problem of a single train, which is formulated as an optimal control problem of nonlinear systems with switching controller. The switching sequence and the switching time are decision variables to be chosen optimally. Generally speaking, it is very difficult to solve this problem analytically due to its nonlinear nature, the complexity of the controller, and the existence of system state and control input constraints. To obtain the numerical solution, by introducing binary functions for every value of the control input, relaxing the binary functions, and imposing a penalty function on the relaxation, the problem is transformed into a parameter optimization problem, which can be efficiently solved by using any gradient-based numerical approach. Then, the authors propose an adaptive numerical approach to solve this problem. Convergence results indicate that any optimal solution of the parameter optimization problem is also an optimal solution of the original problem. Finally, an optimal control problem of a single train illustrates that the adaptive numerical approach proposed by us is less time-consuming and obtains a better cost function value than the existing approaches. [ABSTRACT FROM AUTHOR]

Under the noncascade structure, a permanent-magnet synchronous motor (PMSM) regulates the speed and current in one loop. On the one hand, fast dynamic performance requires large transient current to provide a high torque. On the other hand, unlike a cascade control, the q-axis current is no longer governed by a reference current signal. In such a system, the nominal controllers cannot guarantee that the q-axis current is within the required range. But an excessively large transient current may threaten the circuit safety. To solve the overcurrent protection problem, the ordinary solution is to choose conservative control parameters, but the dynamic performance inevitably suffers a certain degree of loss. In order to improve this drawback, a simple and effective control scheme is introduced with a current-constrained technique. By constructing a special nonlinear gain, the punishment mechanism for the q-axis current is established in the control action directly. The proposed control approach does not impose limitations on the initial state. Moreover, it has good robustness to load torque uncertainty and undergoes rigorous theoretical analysis. Besides, the proposed current-constrained controller has a very concise structure. It yields a higher reliability of the PMSM control system. Comparative simulation and experimental results between the classic PID and the current-constrained controller on the PMSM servo system verify the feasibility of the presented control scheme. [ABSTRACT FROM AUTHOR]

Recently, a number of graph-based approaches have been proposed to detect salient regions in images. Although the graph is essential for these approaches, the graph construction method has not been studied in much detail. We propose a graph construction method that makes better use of multiple Gestalt principles. Specifically, spatial proximity, color similarity, and texture similarity between image regions are employed to choose different edges of the graph. Furthermore, the confliction among multiple Gestalt principles is solved using a primal rank support vector machines algorithm to compute the edge weights. Our experimental results on various salient region detection databases with comparisons to representative approaches demonstrate that the proposed graph construction method helps to detect salient objects in images. [ABSTRACT FROM AUTHOR]

In the paper, we consider the bioprocess system optimal control problem. Generally speaking, it is very difficult to solve this problem analytically. To obtain the numerical solution, the problem is transformed into a parameter optimization problem with some variable bounds, which can be efficiently solved using any conventional optimization algorithms, e.g. the improved Broyden-Fletcher-Goldfarb-Shanno algorithm. However, in spite of the improved Broyden-Fletcher-Goldfarb-Shanno algorithm is very efficient for local search, the solution obtained is usually a local extremum for non-convex optimal control problems. In order to escape from the local extremum, we develop a novel stochastic search method. By performing a large amount of numerical experiments, we find that the novel stochastic search method is excellent in exploration, while bad in exploitation. In order to improve the exploitation, we propose a hybrid numerical optimization algorithm to solve the problem based on the novel stochastic search method and the improved Broyden-Fletcher-Goldfarb-Shanno algorithm. Convergence results indicate that any global optimal solution of the approximate problem is also a global optimal solution of the original problem. Finally, two bioprocess system optimal control problems illustrate that the hybrid numerical optimization algorithm proposed by us is low time-consuming and obtains a better cost function value than the existing approaches. [ABSTRACT FROM AUTHOR]

Time series forecasting is one of the most important issues in numerous applications in real life. The objective of this study was to propose a hybrid neural network model based on wavelet transform (WT) and feature extraction for time series forecasting. The motivation of the proposed model, which is called PCA-WCCNN, is to establish a single simplified model with shorter training time and satisfactory forecasting performance. This model combines the principal component analysis (PCA) and WT with artificial neural networks (ANNs). Given a forecasting sequence, order of the original forecasting model is determined firstly. Secondly, the original time series is decomposed into approximation and detail components by employing WT technique. Then, instead of using all the components as inputs, feature inputs are extracted from all the sub-series obtained from the above step. Finally, based on the extracted features and all the sub-series, a famous neural network construction method called cascade-correlation algorithm is applied to train neural network model to learn the dynamics. As an illustration, the proposed model is compared with two classical models and two hybrid models, respectively. They are the traditional cascade-correlation neural network, back-propagation neural network, wavelet-based cascade-correlation network using all the wavelet components as inputs to establish one model (WCCNN) and wavelet-based cascade-correlation network with combination of each sub-series model (WCCNN multi-models). Results obtained from this study indicate that the proposed method improves the accuracy of ANN and can yield better efficiency than other four neural network models. [ABSTRACT FROM AUTHOR]

This paper studies robust stability of positive switched systems (PSSs) with polytopic uncertainties in both discrete-time and continuous-time contexts. By using multiple linear copositive Lyapunov functions, a sufficient condition for stability of PSSs with dwell time is addressed. Being different from time-invariant multiple linear copositive Lyapunov functions, the Lyapunov functions constructed in this paper are time-varying during the dwell time and time-invariant afterwards. Then, robust stability of PSSs with polytopic uncertainties is solved. All conditions are solvable via linear programming. Finally, illustrative examples are given to demonstrate the validity of the proposed results. [ABSTRACT FROM PUBLISHER]

In the paper, a potential-based policy iteration method is proposed for optimal control of a stochastic dynamic system with an average cost criterion and a parameterized control law. In this method, the potential function and the optimal control parameters are obtained via a least-squares-based approach. The potential estimation algorithm is derived from a temporal difference learning method, which can be viewed as a continuous version of the least-squares policy evaluation algorithm. The policy iteration algorithm is validated by solving a linear quadratic gaussian problem in the simulation. [ABSTRACT FROM AUTHOR]

A class of homogeneous polynomial functions is used to estimate the attractive stability region for an impulsive switched linear system with saturated control input. Under the arbitrary switching rule and the dwell time switching rule, local stabilization conditions are obtained in terms of linear matrix inequalities. The corresponding optimization problems are formulated to obtain a larger attractive stability region. Using the simple ellipsoid method to estimate the attractive stability region produces very conservative results, because the attractive stability region is normally irregular. To solve this problem, a polyhedron constructed using a level set of the homogeneous parameter-dependent quadratic Lyapunov function is used to estimate the attractive stability region. The polyhedron is closer to the attractive stability region than the simple ellipsoid. Finally, numerical examples are given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Robust stabilisation problem of discrete‐time switched linear systems with bounds on the controls and states is investigated in this study. Firstly, the controller synthesis for systems with interval uncertainties which guarantees positivity and stability of the closed‐loop system is studied. These results are then extended to the systems with polytopic uncertainties. All the conditions are formulated in terms of linear feasibility. Finally, numerical examples illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we solve an optimal control problem for switched stochastic systems using calculus of variations, where the objective is to minimize a cost functional defined on the state and the switching times are the sole control variables. In particular, we focus on the problem in which a pre-specified sequence of active subsystems is given. For one switching time case, the derivative of the cost functional with respect to the switching time is derived, which has an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instant. Then, we propose an approach to deal with the problem with multi-switching times case. Finally, two numerical examples are given, highlighting the viability and advantages of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this article, we present a new method to estimate the asymptotic stability regions for a class of nonlinear systems via composite homogeneous polynomial Lyapunov functions, where these nonlinear systems are approximated as a convex hull of some linear systems. Since level set of the composite homogeneous polynomial Lyapunov functions is a union set of several homogeneous polynomial functions, the composite homogeneous polynomial Lyapunov functions are nonconservative compared with quadratic or homogeneous polynomial Lyapunov functions. Numerical examples are used to illustrate the effectiveness of our method. [ABSTRACT FROM PUBLISHER]

In this paper, we consider an optimal co with state and control constraints, where a prespecified sequence of active subsystems is given. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Firstly, we convert the problem into a conventional optimal control problem based on parameterization of the switching instants. Next, through discretizing the control space, applying a time-scaling transformation and using the smoothing technique, the optimal control problem is approximated by a non-linear optimization problem with linear constraints and bounds on the variables. Furthermore, an algorithm that finds a suboptimal solution to the original problem is proposed. One major advantage with the new algorithm implementation is the only need to solve a non-linear optimization problem with linear constraints and bounds on the variables. The gradients of these linear constraints and the objective function can be easily obtained. Therefore, the original optimization problem can be solved efficiently using any gradient-based method, such as sequential quadratic programming algorithm. Finally, a flight planning example illustrates the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of robust H∞ filter design for switched linear discrete-time systems with polytopic uncertainties. The condition of being robustly asymptotically stable for uncertain switched system and less conservative H∞ noise-attenuation level bounds are obtained by homogeneous parameter-dependent quadratic Lyapunov function. Moreover, a more feasible and effective method against the variations of uncertain parameter robust switched linear filter is designed under the given arbitrary switching signal. Lastly, simulation results are used to illustrate the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control problem of switched systems with continuous-time inequality constraints. Because of the complexity of such constraints and switching laws, it is difficult to solve this problem by standard optimization techniques. To overcome the difficulty, we adopt a bi-level algorithm to divide the problem into two nonlinear constrained optimization problems: one continuous and the other discrete. To solve the problem, we transform the inequality constraints into equality constraints which is smoothed using a twice continuously differentiable function and treated as a penalty function. On this basis, the smoothed problem can be solved by any second-order gradient algorithm, e.g., Newton's Method. Finally, numerical examples show that our method is effective compared to existing algorithms. [ABSTRACT FROM AUTHOR]

In this study, a time optimisation problem is solved for a class of linear time‐invariant switched stochastic systems with multi‐switching times using the calculus of variations. The objective of authors' study is to minimise a cost functional defined on the system state, where the sequence of active subsystems is pre‐specified and the switching times are the only control variables. The gradient of the cost functional with respect to the switching times is derived, which has an especially simple form and can be directly used in gradient descent algorithms to locate the optimal switching instants. The proposed method is applied on a two‐tank system, which is a practical example of switched systems. Combining with another numerical example with three switching times case, the viability of the proposed method is further demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, a unified policy iteration approach is presented for the optimal control problem of stochastic system with discounted average cost and continuous state space. The approach consists of temporal difference learning-based potential function approximation algorithms and performance difference formula-based policy improvement. The approximation algorithms are derived by solving the Poisson equation-based fixed-point equation, which can be viewed as continuous versions of least squares policy evaluation algorithm and least squares temporal difference algorithm. The simulations are provided to illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]