Probabilistic constraint tightening techniques for trajectory planning with predictive control

In order for automated mobile vehicles to navigate in the real world with minimal collision risks, it is necessary for their planning algorithms to consider uncertainties from measurements and environmental disturbances. In this paper, we consider analytical solutions for a conservative approximation of the mutual probability of collision between two robotic vehicles in the presence of such uncertainties. Therein, we present two methods, which we call unitary scaling and principal axes rotation, for decoupling the bivariate integral required for efficient approximation of the probability of collision between two vehicles including orientation effects. We compare the conservatism of these methods analytically and numerically. By closing a control loop through a model predictive guidance scheme, we observe through Monte-Carlo simulations that directly implementing collision avoidance constraints from the conservative approximations remains infeasible for real-time planning. We then propose and implement a convexification approach based on the tightened collision constraints that significantly improves the computational efficiency and robustness of the predictive guidance scheme.     

A novel structure for the optimal control of bilateral teleoperation systems with variable time delay

The purpose of designing a controller for a teleoperation system is achieving stability and optimal operation in the presence of factors such as time delay, system disturbance and modeling errors. In this article three new schemes for teleoperation systems are suggested using an optimal control to reduce the error of tracking between the master and slave systems. In the first scheme optimal controller has been designed in both the master and slave subsystems and by a suitable combination of the output signals of both controllers and exerting it to the slave, it has tried to create the best performance with regard to tracking. In the second scheme, as in the first one, optimal controller is applied to both the master and slave systems and the output of each controller is then applied to its own system, and by changing the system parameters and weighting factors, it has tried to reduce the tracking error between the master and the slave subsystems. In the third structure optimal control is applied to the master. In all three structures the positions of master-slave are compared together and controlling signals are applied to the master or slave so that they can track each other in the least possible time. In all schemes the effectiveness of the system is shown through the simulations and they are compared with each other.     

Optimal trajectory exploration large-scale deep reinforcement learning tuned optimal controller for proton exchange membrane fuel cell

To accurately regulate hydrogen flow and guarantee satisfactory output voltage control performance, taking advantage of the high adaptability and robustness of large-scale deep reinforcement learning, an optimal fractional-order proportion integral differential (FOPID) controller for controlling proton exchange membrane fuel cell (PEMFC) output voltage is proposed in this paper. In addition, an optimal trajectory exploration large-scale multi-delay deep deterministic policy gradient (OTEL-MD3PG) algorithm, which naturally considers the baseline FOPID coefficients in the design objective and provides the online coefficient adjusting ability through learning, is designed as the tuner of the controller to improve adaptability and robustness. This algorithm adopts the optimal trajectory exploration policy, whereby a new agent (demonstrator) generates demonstration samples that instruct the agent to learn, and another agent (tracker) adds noise to the action of the demonstrator to explore the limits of its control trajectory, thereby obtaining a more robust control strategy. The simulation results show that this proposed algorithm offers a rapid response, strong anti-interference, and excellent control performance.     

Single landmark feedback-based time optimal navigation for a differential drive robot

In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.     

A direct measurement method of quantum relaxation time

The quantum relaxation time of electrons in condensed matters is an important physical property, but its direct measurement has been elusive for a century. Here, we report a breakthrough that allows direct determination of quantum relaxation time at zero and non-zero frequencies using optical measurement. Through dielectric loss function, we connect bound electron effects to the physical parameters of plasma resonance and find an extra term of quantum relaxation time from inelastic scattering between bound electrons and conduction electrons at non-zero frequencies. We demonstrate here that the frequency-dependent inelastic polarization effect of bound electrons is the dominant contribution to quantum relaxation time of conduction electrons at optical frequencies, and the elastic polarization effect of bound electrons also dramatically changes the plasma resonance frequency through effective screening to charge carriers.     

A composite pseudospectral method for solving multi-delay optimal control problems involving piecewise constant delay functions

An adaptive numerical method for solving multi-delay optimal control problems with piecewise constant delay functions is introduced. The proposed method is based on composite pseudospectral method using the well-known Legendre–Gauss–Lobatto points. In this approach, the main problem converts to a mathematical optimization problem whose solution is much more easier than the original one. The necessary conditions of optimality associated to nonlinear piecewise constant delay systems are derived. The method is easy to implement and provides very accurate results.     

A control algorithm for systems with dead time

A least squares control algorithm for single-input single-output (SISO) systems is developed. The algorithm allows for a delay with large dead time and uses proportional- integral-derivative actions in their parallel form to achieve steady-state without error. Optimization of the controller parameters is achieved and the parameters of the controller are determined from the solution of a set of linear simultaneous equations. The control strategy is to optimize the controller parameters such that a desired well-behaved trajectory is obtained. The controller is shown to be robust and the algorithm is shown to function as well without or with large dead time, to have low sensitivity to changes in the dead time, and to allow an adaptive estimation of changing system parameters. The application of the developed algorithm to control the glucoregulatory system, based on a 4th-order digital model, is presented in two cases: free time delay and with large dead time.     

A novel design method for optimal IIR system identification using opposition based harmony search algorithm

In this paper a population based evolutionary optimization methodology called Opposition based Harmony Search Algorithm (OHS) is applied for the optimization of system coefficients of adaptive infinite impulse response (IIR) system identification problem. The original Harmony Search (HS) algorithm is chosen as the parent one and opposition based approach is applied to it with an intention to exhibit accelerated near global convergence profile. During the initialization, for choosing the randomly generated population/solution opposite solutions are also considered and the fitter one is selected as apriori guess for having faster convergence profile. Each solution in Harmony Memory (HM) is generated on the basis of memory consideration rule, a pitch adjustment rule and a re-initialization process which gives the optimum result corresponding to the least error fitness in multidimensional search space. Incorporation of different control parameters in basic HS algorithm results in balancing of exploration and exploitation of search space. The proposed OHS based system identification approach has alleviated from inherent drawbacks of premature convergence and stagnation, unlike Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed OHS based system identification approach over GA, PSO and DE in terms of convergence speed, identifying the system plant coefficients and mean square error (MSE) fitness values produced for both same order and reduced order models of adaptive IIR filters.     

Orthogonal functions approach to optimal control of delay systems with reverse time terms

Using block-pulse functions (BPFs)/shifted Legendre polynomials (SLPs) a unified approach for computing optimal control law of linear time-varying time-delay systems with reverse time terms and quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamical systems are converted into linear algebraic equations by using operational matrices of orthogonal functions (BPFs and SLPs). The problem of finding optimal control law is thus reduced to the problem of solving algebraic equations. One example is included to demonstrate the applicability of the proposed approach.     

Observer based sliding mode controller for vehicles with roll dynamics

In this work, considering the roll dynamics and actuator dynamics, an observer-based control scheme for a vehicle is proposed. The proposal considers a nonlinear higher order sliding mode observer to estimate unmeasurable lateral velocity, roll angle and roll velocity. Using the observer information, a controller based on block control with sliding mode technique is designed for the reference trajectory tracking of the lateral and yaw velocities of the vehicle. The stability of the complete closed-loop system including zero dynamics is analyzed. The effectiveness of the proposed scheme is demonstrated through CarSim simulations.     

An adaptive mesh method with variable relaxation time

Moving mesh partial differential equations have been widely used in the last decade for solving differential equations exhibiting large solution variations such as shock waves and boundary layers.In this paper, we have applied a dynamic adaptive method for solving time-dependent differential equations. The mesh velocities are governed by an equation in which a relaxation time is employed to move nodes in such a way that they remain concentrated in regions of rapid variation of the solution. A numerical example involving a blow-up problem shows the advantage of using a variable relaxation time over a fixed one.     

A combined time and frequency domain method for model reduction of discrete systems

A new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented. First, the z-transfer functions are transformed into the w-domain by the bilinear transformation, z = (1+w)/(1?w). Then, four model reduction methods—Routh approximation, Hurwitz polynomial approxima- tion, stability equation, and retaining dominant poles—are used respectively to reduce the order of the denominator polynomials in the w-domain. Least squares estimate is then used to find the optimal coefficients in the numerator polynomials of the reduced models so that the unit step response errors are reduced to a minimum. The advantages of the proposed method are that both frequency domain and time domain characteristics of the original systems can be preserved in the reduced models, and the reduced models are always stable provided the original models are stable.     

Bond graph formulation of an optimal control problem for linear time invariant systems

A recent communication has proposed a conjectural procedure for representing a category of optimal control problems in bond graph language [W. Marquis-Favre, B. Chereji, D. Thomasset, S. Scavarda, Bond graph representation of an optimal control problem: the dc motor example, in: ICBGM’05 International Conference of Bond Graph Modelling and Simulation, New Orleans, USA, January 23-27, 2005, pp. 239-244]. This paper aims at providing a fundamental theory for proving the effectiveness of this procedure. The class of problem that the procedure can deal with has been extended. Its application was formerly restricted to linear time invariant siso system. The systems considered now are linear time invariant mimo systems. The optimization objective is the minimization of dissipation and input. The developments concerning the optimal control problem are based on the Pontryagin maximum principle and the proof of the effectiveness of the procedure makes a broad use of the port-Hamiltonian concept. As a result, the bond graph representation of the given optimization problem enables the analytical system, which provides the optimal solution, to be derived. The work presented in this paper is the first step in research with perspectives towards formulating dynamic optimization problems in bond graph and, towards coupling this formulation with a sizing methodology using bond graph language and a state-space inverse model approach. This sizing methodology, however, is not the topic of this paper and thus is not presented here.     

CALIMERA: A new early time series classification method

Early time series classification is a variant of the time series classification task, in which a label must be assigned to the incoming time series as quickly as possible without necessarily screening through the whole sequence. It needs to be realized on the algorithmic level by fusing a decision-making method that detects the right moment to stop and a classifier that assigns a class label. The contribution addressed in this paper is twofold. Firstly, we present a new method for finding the best moment to perform an action (terminate/continue). Secondly, we propose a new learning scheme using classifier calibration to estimate classification accuracy. The new approach, called CALIMERA, is formalized as a cost minimization problem. Using two benchmark methodologies for early time series classification, we have shown that the proposed model achieves better results than the current state-of-the-art. Two most serious competitors of CALIMERA are ECONOMY and TEASER. The empirical comparison showed that the new method achieved a higher accuracy than TEASER for 35 out of 45 datasets and it outperformed ECONOMY in 20 out of 34 datasets.     

A new direct method based on the Chebyshev cardinal functions for variable-order fractional optimal control problems

In this paper, a new direct method based on the Chebyshev cardinal functions is proposed to solve a class of variable-order fractional optimal control problems (V-OFOCPs). To this end, a new operational matrix (OM) of variable-order (V-O) fractional derivative in the Caputo sense is derived for these basis functions and is used to obtain an approximate solution for the problem under study. In the proposed method, the state and the control variables are expanded in terms of the Chebyshev cardinal functions with unknown coefficients, at first. Then, the OM of V-O fractional derivative and some properties of the Chebyshev cardinal functions are employed to achieve a nonlinear algebraic equation corresponding to the performance index and a nonlinear system of algebraic equations corresponding to the dynamical system in terms of the unknown coefficients. Finally, the method of constrained extremum is applied, which consists of adjoining the constraint equations derived from the given dynamical system and the initial conditions to the performance index by a set of undetermined Lagrange multipliers. As a result, the necessary conditions of optimality are derived as a system of algebraic equations in the unknown coefficients of the state variable, control variable, and Lagrange multipliers. Furthermore, some numerical examples of different types are demonstrated with their approximate solutions for confirming the high accuracy and applicability of the proposed method.     

A direct approach using the finite element method for the solution of the linear optimal control problem with a quadratic criterion

The present paper proposes a numerical approach to a linear optimal control problem with a quadratic performance index. In this technique, the time interval is divided into a number of time segments and all of the unknown functions which appear in the performance index are either interpolated linearly with respect to time or assumed to be constant in each time segment. The augmented performance index is discretized within each time element through the ordinary finite element technique.The main advantage of the present method is as follows: all of the necessary conditions for the performance index to be stationary can be expressed in the form of algebraic equations and the performance sequence of the state variables can be eliminated. As a result, the optimal control problem is reduced to the simple one of finding the sequence of control variables alone, which minimizes the quadratic performance index.A general formulation of the method is given and simple numerical examples are shown to demonstrate the effectiveness of the technique.     

基于脉冲积累的SAR实时聚焦算法

在实际的SAR场景中,由于载机平台运动的不规律会引入相位误差,这将导致SAR图像出现模糊,甚至不能形成图像,因此需要准确地估计和补偿相位误差.提出一种较好的SAR相位历史估计算法,在方位向应用延时自相关方法进行准确的相位估计,由此实现SAR的准确聚焦成像.该相位估计方法具有较高的计算效率,非常适合于实时SAR系统.利用对实际SAR数据的聚焦处理证明了该方法的有效性.     

A new data mining method for time series in visual analysis of regional economy

In order to improve the effect of visual analysis of regional economy, this paper uses machine learning algorithms to analyze time series data, uses various models and methods of intelligent data analysis to mine data laws from huge data, statistical data reports, and find problems in economic development. Moreover, this paper combines the time series algorithm to design and plan the functional structure of the system, and design a separate module structure from the actual situation of regional economic analysis, and build a model system from the overall structure. After constructing the system, this paper tests the system. From the results of the experimental research, we can see that the regional economic visualization system based on time series constructed in this paper has perfect system functions and can meet the needs of regional economic analysis.     

Layer,Lie algebraic method of motion planning for nonholonomic systems

In this paper a layer, Lie algebraic method of motion planning for nonholonomic systems is presented. It plans locally a motion towards a goal by searching for optimal directions in equi-cost spaces. The spaces are easy to determine via exploiting Lie algebraic properties of vector fields that define the controlled system. The method was illustrated on the unicycle robot and the inverted pendulum.