Low-complexity Controllers Research Articles

Nonholonomic dynamics and control of road vehicles: moving toward automation

Nonholonomic models of automobiles are developed by utilizing tools of analytical mechanics, in particular the Appellian approach that allows one to describe the vehicle dynamics with minimum number of time-dependent state variables. The models are categorized based on how they represent the wheel-ground contact, whether they incorporate the longitudinal dynamics, and whether they consider the steering dynamics. It is demonstrated that the developed models can be used to design low-complexity controllers that enable automated vehicles to execute a large variety of maneuvers with high precision.

Padé Approximation and Hypergeometric Functions: A Missing Link with the Spectrum of Delay-Differential Equations

It is well known that rational approximation theory involves degenerate hyperge-ometric functions and, in particular, the Padé approximation of the exponential function is closely related to Kummer hypergeometric functions. Recently, in the context of the study of the exponential stability of the trivial solution of delay-differential equations, a new link between the degenerate hypergeometric function and the zeros distribution of the characteristic function associated with linear delay-differential equations was emphasized. Such a link allowed the characterization of a property of time-delay systems known as multiplicity-induced-dominancy (MID), which opened a new direction in designing low-complexity controllers for time-delay systems by using a partial pole placement idea. Thanks to their relations to hypergeometric functions, we explore in this paper links between the spectrum of delay-differential equations and Padé approximations of the exponential function. This note exploits and further comments recent results from [I. Boussaada, G. Mazanti and S-I. Niculescu. 2022, Comptes Rendus. Mathématique] and [I. Boussaada, G. Mazanti and S-I. Niculescu. 2022, Bulletin des Sciences Mathématiques].

Attitude Tracking Control of Small-Scale Unmanned Helicopters Using Quaternion-Based Adaptive Dynamic Surface Control

In this paper, a quaternion-based adaptive dynamic surface control method is proposed for attitude tracking control for small-scale unmanned helicopters with external disturbance and uncertain dynamics. The quaternion formalism is introduced and a quaternion-based multi-input-multi-output nonlinear model is derived from the attitude dynamics of a small-scale helicopter. The low-complexity controllers are designed by the dynamic surface control method as it eliminates the problem of the explosion of items. The singularity problem is avoided by substituting Euler kinematic equations in the nonlinear model with quaternion expressions and integrating the quaternion expressions into the design process of the dynamic surface control. For improving the robustness of the control system, the radial basis function networks are applied to approximate the uncertain dynamics. The external disturbance is also compensated in the controllers’ design. This paper proves that the proposed method can guarantee the uniformly ultimate boundness of this attitude system. Simulation results are presented finally and show the effectiveness of this control approach.

Practical Guidelines for Tuning PD and PI Delay-Based Controllers

This paper focuses on the design of two different delay-based control schemes. These two low-complexity controllers are proposed as alternatives for the classical PD and PI controllers. More precisely, first, we study a PD controller using the Euler approach for approximating the derivative action. Second, we analyze the implications of imposing a delay in the error signal on the integral action of the PI controller for closed-loop response manipulation purposes. Our main contribution lies in proposing some practical guidelines for the tuning of these delayed control schemes such that the closed-loop system is stable. To this end, the criteria developed in this work makes use of the well-known D—partition method, with the difference that we propose a simple criterion to detect stabilizing regions, avoiding in this way the crossing direction analysis. Several numerical examples illustrate the effectiveness of the proposed approach.

Control Difuso con Estimador de Estados para Sistemas de Páncreas Artificial

A fuzzy controller for a minimal states model is proposed to achieve a continuous and effcient insulin infusion in patients with Type 1 Diabetes. An Extended Kalman Filter is also applied to supply the deficiencies of the current glucose sensor technologies and estimate residual insulin in the system to predict future behavior. The controller is tuned manually and iteratively, and achieves closed-loop responses of glycemia constrained between [80,140] (mgdl), with a mean of 117, 6 (mgdl) and a standard deviation of 11, 3 (mgdl) over a whole year ensemble of 24-hour system responses with 4 meal intakes per day. These results show that is possible to design low complexity controllers that are easily tunable by experienced users or physicians focusing on a closed-loop system response analysis. Also, the combination of heuristic and model-based techniques allows to synthesize robust controllers for real application situations and, furthermore, effciently manage the insulin usage. Nevertheless, the actual application of a closed-loop system on a human being should require higher dimension models to fit different situations, a proven robust controller and wide adaptability to different patients and their meal intake routine.

Low-complexity control of hybrid systems using approximate multi-parametric MILP

Control of hybrid systems faces computational complexity as a main challenging problem. To reduce the computational burden, multi-parametric programming has been proposed to obtain the explicit solution of the optimal control problems for some classes of hybrid systems. This strategy provides the solution as a function of the state variables which can be obtained in an off-line fashion. A shortcoming of this technique is that the complexity of the explicit solution is again prohibitive for large problems. The main contribution of this paper is the introduction of an approximation algorithm for solving a general class of multi-parametric mixed-integer linear programming (mp-MILP) problems. The algorithm selects those binary sequences that make significant improvement in the objective function, if considered. It is shown that significant reduction in computational complexity can be achieved by introducing adjustable level of suboptimality. A family of suboptimal controllers is obtained by the proposed approach for which the level of error and complexity can be adjusted by a tuning parameter. It is shown that no part of the parameter space is disregarded during the approximation. Also it is proved that the error in the achieved approximate solutions is a monotonically increasing function of the tuning parameter. Assuming that the closed-loop stability is ensured by including some constraints in the formulation of hybrid control, it will be preserved by the suboptimal low-complexity controllers. Illustrative examples are presented to demonstrate the achieved complexity reduction.

Low-complexity quantized switching controllers using approximate bisimulation

In this paper, we consider the problem of synthesizing low-complexity controllers for incrementally stable switched systems. For that purpose, we establish a new approximation result for the computation of symbolic models that are approximately bisimilar to a given switched system. The main advantage over existing results is that it allows us to design naturally quantized switching controllers for safety or reachability specifications; these can be pre-computed offline and therefore the online execution time is reduced. Then, we present a technique to reduce the memory needed to store the control law by borrowing ideas from algebraic decision diagrams for compact function representation and by exploiting the non-determinism of the synthesized controllers. We show the merits of our approach by applying it to a simple model of temperature regulation in a building.

Evolution of low-complexity neural controllers based on multiobjective evolution

In this paper, we present a new method based on multiobjective evolutionary algorithms to evolve low-complexity neural controllers for agents that have to perform multiple tasks simultaneously. In our method, each task and the structure of the neural controller are considered as separated objective functions. We compare the results of two different encoding schemes: (1) connectionist encoding, and (2) node-based encoding. The results show that multiobjective evolution can be successfully applied to generate low-complexity neural controllers. In addition, node-based encoding outperformed connectionist encoding in terms of agent performance and the robustness of the neural controller.

Comparison of Low-complexity Controllers in Varying Time-delay Systems

Motivated by the recent developments in networked control systems and control over wireless, this paper presents a comparison of five control algorithms that are based on PID, IMC and fuzzy gain scheduling techniques and discusses their performance in varying time-delay systems. The low complexity of the proposed algorithms makes their use attractive in resource-constrained environments such as wireless sensor and actuator networks. The control system consists of a controller, a simple process and an output delay in the feedback loop. Three different delay models are considered in this framework; constant, random, and correlated random delay. In addition to presenting modifications to the control algorithms to better fit the varying time-delay systems a delay-robust tuning method is proposed, and the performance of various controllers is evaluated using simulation. The results show the benefits of adapting the controller parameters based on delay measurement if its amplitude is significant with respect to the time-constant of the process. Nevertheless, the PID algorithm used in the study also performs well in all scenarios, and this is achieved by its careful tuning.

From experiment design to closed-loop control

The links between identification and control are examined. The main trends in this research area are summarized, with particular focus on the design of low complexity controllers from a statistical perspective. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made as this ensures the best statistical accuracy. This does not necessarily mean that a full-order model always is necessary as well designed experiments allow for restricted complexity models to be near-optimal. Experiment design can therefore be seen as the key to successful applications. For this reason, particular attention is given to the interaction between experimental constraints and performance specifications.

From experiments to closed loop control

In this paper we examine the links between identification and control. The main trends in this research area are summarized, with particular focus on design of low complexity controllers. It is argued that a guiding principle should be to model as well as possible before any model or controller simplifications are made, as this ensures the best statistical accuracy. Particular attention is given to the experiment design issue since well-designed experiments facilitates this task. Furthermore, the interaction between experimental constraints and performance specifications is discussed.

Neurofuzzy state estimators and their applications

Neurofuzzy algorithms have been extensively developed in recent years for the real time/online identification of nonlinear a priori unknown dynamical processes. As with all rule base paradigms they suffer from the curse of dimensonality, restricting their practical use to low dimensional control problems. This paper shows how adaptive construction algorithms based on additive decomposition techniques can overcome this problem, to produce parsimonious neurofuzzy models which retain their transparency or interpretability. Not only does this approach extend the applicability of neurofuzzy algorithms, it also enables low complexity controllers and estimators to be derived. In this context neurofuzzy state estimators are derived, which automatically parameterise a Kalman filter for a process state estimate reconstruction from any input/output data source. This approach avoids pitfalls of the extended Kalman filter, and is optimal for local models. The paper discusses real world applications of this new theory of modelling and estimation to helicopter guidance, intelligent driver warning system, communication antennas, autonomous underwater vehicles, ship collision avoidance guidance, and an IFAC benchmark problem.

Neurofuzzy State Estimators and their Applications

Neurofuzzy algorithms have been extensively developed in recent years for the real time/online identification of nonlinear a priori unknown dynamical processes. As with all rule base paradigms they suffer from the curse of dimensionality, restricting their practical use to low dimensional control problems. This paper shows how adaptive construction algorithms based on additive and extended additive decomposition techniques can overcome this problem, to produce parsimonious neurofuzzy models which retain their transparency or interpretability. Not only does this approach extend the applicability of neurofuzzy algorithms, it also enables low complexity controllers, estimators to be derived. In this context neurofuzzy state estimators are derived which automatically parameterise a Kalman filter for a process state estimate reconstruction from any input/output data source. This approach avoids pitfalls of the extended Kalman filter, and is optimal for local models. The paper discusses real world applications of this new theory of modelling and estimation to helicopter guidance, intelligent driver warning system, communication antennas, autonomous underwater vehicles and an IFAC benchmark problem.

Low Order Control Design by Feedback Relevant Identification and Closed Loop Controller Reduction

Abstract An approach is presented that can be used to obtain low complexity controllers for an unknown system. In this approach, the identification of a set of models is used to represent the incomplete knowledge of the system. Subsequently, the set is used for the synthesis of a robust controller. In order to design low complexity controllers, the aim is to find a low complexity representation of the set. Additionally, a closed loop reduction tool can be used to decrease the controller complexity further. This approach will be illustrated by an application to a multivariable positioning mechanism present in a wafer stepper.

Low Order Suboptimal Robust Controller Design for Systems with Structured Uncertainty

Abstract This paper considers the problem of designing robust controllers for linear plants affected by rank one real perturbations. The main objective of the paper is to use a convex parameterization of robustly stabilizing controllers for optimizing the stability margin over an assigned class of low complexity controllers. In fact, it is well known that if no constraints on the controller structure are imposed, the complexity of the resulting optimal controller is usually excessive. In this paper, a procedure is proposed which allows one to select a suboptimal controller within a fixed class, by solving a sequence of linear matrix inequalities feasibility problems. Several application examples are reported to discuss the performance of the proposed procedure.