An iterative learning approach to formation control of multi-agent systems

In this paper, an efficient framework is proposed to the formation control problem of multiple agents with unknown nonlinear dynamics, by means of the iterative learning approach. In particular, a distributed D-type iterative learning scheme is developed for the multi-agent system with switching topology, whose switching time and sequence are allowed to be varied at different iterations according to the actual trajectories of agents, and a sufficient condition is derived to ensure that the desired formation can be always preserved from the initial starting location to the final one after some iterations. Simulation results are provided to verify the effectiveness of the proposed approach.     

An algebraic approach to supervisory control

Supervisory control problems are formulated in terms of a process model where the mechanism of control is expressed in terms of an algebraic operator with the plant and supervision processes as its arguments. The solution subspaces for supervisory processes restrict the observation and the control capability of supervision. The main result corresponds to decentralized marked supervision under partial observations, and specific cases are derived from this result in a unified, algebraic way. The result and its derivation demonstrate the relative simplicity of the algebraic process formulation.     

An inverse-model approach to multivariable norm optimal iterative learning control with auxiliary optimisation

Motivated by the commonly encountered problem in which tracking is only required at selected intermediate points within the time interval, a general optimisation-based iterative learning control (ILC) algorithm is derived that ensures convergence of tracking errors to zero whilst simultaneously minimising a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. In practice, the proposed solutions enable a repeated tracking task to be accurately completed whilst simultaneously reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear. The theory is developed using the well-known norm optimal ILC (NOILC) framework, using general linear, functional operators between real Hilbert spaces. Solutions are derived using feedforward action, convergence is proved and robustness bounds are presented using both norm bounds and positivity conditions. Algorithms are specified for both continuous and discrete-time state-space representations, with the latter including application to multi-rate sampled systems. Experimental results using a robotic manipulator confirm the practical utility of the algorithms and the closeness with which observed results match theoretical predictions.     

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.     

An LMI approach for robust iterative learning control with quadratic performance criterion

This paper presents the design of iterative learning control based on quadratic performance criterion (Q-ILC) for linear systems subject to additive uncertainty. The robust Q-ILC design can be cast as a min–max problem. We propose a novel approach which employs an upper bound of the worst-case performance, then formulates a non-convex quadratic minimization problem to get the update of iterative control inputs. Applying Lagrange duality, the Lagrange dual function of the non-convex quadratic problem is equivalent to a convex optimization over linear matrix inequalities (LMIs). An LMI algorithm with convergence properties is then given for the robust Q-ILC design. Finally, we provide a numerical example to illustrate the effectiveness of the proposed method.     

An extended PID type iterative learning control

This paper presents a new iterative learning control (ILC) for discrete-time single-input single-output (SISO) linear time-invariant (LTI) systems. To establish this ILC, the input of the controlled system is modified by using a novel four-parametric algorithm. This algorithm is called the extended proportional plus integral and derivative (EPID) type, since by eliminating the fourth parameter of it one would get to the PID type ILC, therefore PID type ILC is a special case of it. The convergence of the proposed ILC is analyzed and an optimal method is presented to determine its parameters. It is shown that the given ILC has a better performance than the PID-type one. Three illustrative examples are included to demonstrate the effectiveness and the preference of the presented ILC.     

An iterative optimization approach to design of control Lyapunov function

This paper presents a fractional programming formulation and its solution strategy for design of control Lyapunov function (CLF) to guarantee the closed-loop stability of a control affine system for the states in a specified region. Without restrictive assumptions found in previous approaches, the fractional programming problem is reformulated as a recursive optimization problem to solve for a CLF with basis functions. A computationally effective derivative-free coordinate search method is proposed to find the solution, where the search space is confined by a piecewise linear function that approximates the lower bound of objective function. A CLF-based controller design is also proposed to handle infinity-norm input constraints. Two examples with actuator saturation and state constraints demonstrate the efficacy of the proposed approach.     

Formation control of discrete-time multi-agent systems by iterative learning approach

In this paper, the formation control problem is investigated for discrete-time multi-agent systems with unknown nonlinear dynamics by means of the iterative learning approach. For networks with switching topology, a distributed iterative learning scheme is developed using the local formation error data with anticipation in time, and a sufficient condition is derived to guarantee that the desired formation can be preserved during the whole finite-time motion or operation process, even in the presence of initial formation errors. Simulation results illustrate the effectiveness of the proposed method.     

An iterative approach to the optimal co-design of linear control systems

This paper investigates the optimal co-design of both physical plants and control policies for a class of continuous-time linear control systems. The optimal co-design of a specific linear control system is commonly formulated as a nonlinear non-convex optimisation problem (NNOP), and solved by using iterative techniques, where the plant parameters and the control policy are updated iteratively and alternately. This paper proposes a novel iterative approach to solve the NNOP, where the plant parameters are updated by solving a standard semi-definite programming problem, with non-convexity no longer involved. The proposed system design is generally less conservative in terms of the system performance compared to the conventional system-equivalence-based design, albeit the range of applicability is slightly reduced. A practical optimisation algorithm is proposed to compute a sub-optimal solution ensuring the system stability, and the convergence of the algorithm is established. The effectiveness of the proposed algorithm is illustrated by its application to the optimal co-design of a physical load positioning system.     

An algebraic approach to shape-from-image problems

This paper presents a new method for recovering three-dimensional shapes of polyhedral objects from their single-view images. The problem of recovery is formulated in a constrained optimization problem, in which the constraints reflect the assumption that the scene is composed of polyhedral objects, and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture. For practical purpose it is decomposed into the two more tractable problems: a linear programming problem and an unconstrained optimization problem. In the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra, whereas similar constraints have usually been represented in terms of a gradient space. Moreover, superstrictness of the constraints can be circumvented by a new concept ‘position-free incidence structure’. For this reason the present method has several advantages: it can recover the polyhedral shape even if image data are incorrect due to vertex-position errors, it can deal with perspective projection as well as orthographic projection, the number of variables in the optimization problem is very small (three or a little greater than three), and any kinds of surface information can be incorporated in a unifying manner.     

An algebraic approach to feature interactions

The various approaches proposed to provide communication between CAD systems and process planning systems share the major problem that, due to geometric interactions among features, there may be several equally valid sets of manufacturable features describing the same part, and different sets of features may differ in their manufacturability. Thus, to produce a good process plan-or, in some cases, any plan at ll-it may be necessary to interpret the part as a different set of features than the one initially obtained from the CAD model. This is addressed using an algebra of features. Given a set of features describing a machinable part, other equally valid interpretations of the part can be produced by performing operations in the algebra. This will enable automated process planning systems to examine these interpretations in order to see which one is most appropriate for use in manufacturing. The feature algebra has been implemented for a restricted domain and integrated with the Protosolid solid modeling system and the EFHA process planning system     

A non-standard iterative learning control approach to tracking periodic signals in discrete-time non-linear systems

In this paper we use the formalism of iterative learning control (ILC) to solve the repetitive control problem of forcing a system to track a prescribed periodic reference signal. Although the systems we consider operate continuously in time, rather than with trials that have distinct starting and ending times, we use the ILC approach by defining a 'trial' in terms of completion of a single 'period' of the output trajectory, where a period is an interval from the start of the trial until the system returns to its initial state. The ILC scheme we develop does not use the standard assumption of uniform trial length. In the final result the periodic motion is achieved by 'repetition' of the learned ILC input signal for a single period. Analysis of the convergence of the algorithm uses an intermediate convergence result for the typical ILC problem. This intermediate result is based on a multi-loop control interpretation of the signal flow in ILC. The idea is demonstrated on an example and it is noted that it may be possible to generalize the ideas to broader classes of systems and ILC algorithms.     

A pseudoinverse-based iterative learning control

Learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time. In this paper, an iterative learning control (ILC) algorithm is proposed to accommodate a general class of nonlinear, nonminimum-phase plants with disturbances and initialization errors. The algorithm requires the computation of an approximate inverse of the linearized plant rather than the exact inverse. An advantage of this approach is that the output of the plant need not be differentiated. A bound on the asymptotic trajectory error is exhibited via a concise proof and is shown to grow continuously with a bound on the disturbances. The structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components     

Convex modifications to an iterative learning control law

In this paper, a predictive norm-optimal iterative learning control algorithm from Amann, Owens, and Rogers (Int. J. Control 69 (2) (1998) 203-226) is analyzed. The main new result of this is that any of the predictive inputs from the predictive algorithm can be used in the control of the plant. This results in a faster convergence rate than that obtained with the approach proposed by Amann, Owens, and Rogers. Furthermore, the nature of the convergence of this new scheme is analysed in detail in terms of the free parameters of the algorithm.     

A computationally efficient norm optimal iterative learning control approach for LTV systems

This paper proposes a computationally efficient iterative learning control (ILC) approach termed non-lifted norm optimal ILC (N-NOILC). The objective is to remove the computational complexity issues of previous 2-norm optimal ILC approaches, which are based on lifted system techniques, while retaining the iteration domain convergence properties. The computational complexity needed to implement the proposed method scales linearly with the trial length. Therefore, the approach can be implemented on controlled processes having long trial durations and high sampling rates. Robustness is accomplished by adding a penalty term on the control input in the cost function. Simulations are presented to verify and validate the features of the proposed method.     

Networked iterative learning control approach for nonlinear systems with random communication delay

This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.     

高阶无模型自适应迭代学习控制

针对一类非线性非仿射离散时间系统,提出了高阶无模型自适应迭代学习控制方案.控制器的设计和分析仅依赖于系统的输入/输出(I/O)数据,不需要已知任何其他知识.该方法采用了高阶学习律,可利用更多以前重复过程中的控制信息提高系统收敛性,且学习增益可通过"拟伪偏导数"更新律迭代调节.仿真结果验证了所提出算法的有效性.     

All-pass filtering in iterative learning control

In iterative learning control (ILC), it is highly desirable to have a learning compensator with a unit-gain for all frequencies, in order to avoid noise amplification and learning speed degradation during the learning process. In this paper, we show that the realization of a unit-gain compensator is straightforward in ILC, using both forward and backward filtering. As an illustrative example, a unit-gain derivative is proposed to overcome the drawbacks of the conventional derivative. The proposed scheme is equivalent to an all-pass unit-gain phase shifter; the forward filtering uses a 0.5-order derivative and the backward filtering employs a 0.5-order integral. The all-pass phase shifter is deployed in a unit-gain D-type ILC. The advantages of the unit-gain feature are demonstrated by some experimental results on a robot manipulator.     

Parameter optimization in iterative learning control

In this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law. With this new algorithm, monotonic convergence of the error to zero is guaranteed if the original system is a discrete-time LTI system and it satisfies a positivity condition. If the original system is not positive, two methods are derived to make the system positive. The effect of the choice of weighting parameters in the performance index on convergence rate is analysed. As a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm. A high-order version of the algorithm is also derived and its convergence analysed. The theoretical findings in this paper are highlighted with simulations.