An LMI approach to control-oriented identification and model (In) validation of LPV systems

This note proposes a control-oriented identification framework for a class of linear parameter varying systems that takes into account both the dependence of part of the model on time-varying parameters as well as the possible existence of a nonparametric component. The main results of the note show that the problems of obtaining and validating a model for these systems can be recast as linear matrix inequality feasibility problems. Moreover, as the information is completed, the algorithm is shown to converge in the l/sub 2/-induced topology to the actual plant. Additional results include deterministic bounds on the identification error. These results are illustrated with a practical example arising in the context of active vision.     

Performance benchmarking of quadrotor systems using time-optimal control

Frequently hailed for their dynamical capabilities, quadrotor vehicles are often employed as experimental platforms. However, questions surrounding achievable performance, influence of design parameters, and performance assessment of control strategies have remained largely unanswered. This paper presents an algorithm that allows the computation of quadrotor maneuvers that satisfy Pontryagin’s minimum principle with respect to time-optimality. Such maneuvers provide a useful lower bound on the duration of maneuvers, which can be used to assess performance of controllers and vehicle design parameters. Computations are based on a two-dimensional first-principles quadrotor model. The minimum principle is applied to this model to find that time-optimal trajectories are bang-bang in the thrust command, and bang-singular in the rotational rate control. This paper presents a procedure allowing the computation of time-optimal maneuvers for arbitrary initial and final states by solving the boundary value problem induced by the minimum principle. The usage of the computed maneuvers as a benchmark is demonstrated by evaluating quadrotor design parameters, and a linear feedback control law as an example of a control strategy. Computed maneuvers are verified experimentally by applying them to quadrocopters in the ETH Zurich Flying Machine Arena testbed.     

Optimization-based iterative learning for precise quadrocopter trajectory tracking

Current control systems regulate the behavior of dynamic systems by reacting to noise and unexpected disturbances as they occur. To improve the performance of such control systems, experience from iterative executions can be used to anticipate recurring disturbances and proactively compensate for them. This paper presents an algorithm that exploits data from previous repetitions in order to learn to precisely follow a predefined trajectory. We adapt the feed-forward input signal to the system with the goal of achieving high tracking performance—even under the presence of model errors and other recurring disturbances. The approach is based on a dynamics model that captures the essential features of the system and that explicitly takes system input and state constraints into account. We combine traditional optimal filtering methods with state-of-the-art optimization techniques in order to obtain an effective and computationally efficient learning strategy that updates the feed-forward input signal according to a customizable learning objective. It is possible to define a termination condition that stops an execution early if the deviation from the nominal trajectory exceeds a given bound. This allows for a safe learning that gradually extends the time horizon of the trajectory. We developed a framework for generating arbitrary flight trajectories and for applying the algorithm to highly maneuverable autonomous quadrotor vehicles in the ETH Flying Machine Arena testbed. Experimental results are discussed for selected trajectories and different learning algorithm parameters.     

Design of full state feedback finite‐precision controllers

In this paper, the Generalized L2 Synthesis framework is brought to bear on the problem of control design of full state feedback finite‐precision controllers. In particular, we investigate the problem of designing full state feedback controllers that achieve guaranteed H‐infinity performance objectives, subject to finite precision constraints on the controller. It is shown that by adopting the Generalized L2 Synthesis framework, the errors in the controller implementation can be captured as full structured uncertainty, and computationally tractable linear matrix inequality techniques used for analysis and synthesis. Copyright © 2002 John Wiley & Sons, Ltd.     

Patch models and their applications to multivehicle command and control.

We introduce patch models, a computational modeling formalism for multivehicle combat domains, based on spatiotemporal abstraction methods developed in the computer science community. The framework yields models that are expressive enough to accommodate nontrivial controlled vehicle dynamics while being within the representational capabilities of common artificial intelligence techniques used in the construction of autonomous systems. The framework allows several key design requirements of next-generation network-centric command and control systems, such as maintenance of shared situation awareness, to be achieved. Major features include support for multiple situation models at each decision node and rapid mission plan adaptation. We describe the formal specification of patch models and our prototype implementation, i.e., Patchworks. The capabilities of patch models are validated through a combat mission simulation in Patchworks, which involves two defending teams protecting a camp from an enemy attacking team.     

A model (in)validation approach to gait classification

This paper addresses the problem of human gait classification from a robust model (in)validation perspective. The main idea is to associate to each class of gaits a nominal model, subject to bounded uncertainty and measurement noise. In this context, the problem of recognizing an activity from a sequence of frames can be formulated as the problem of determining whether this sequence could have been generated by a given (model, uncertainty, and noise) triple. By exploiting interpolation theory, this problem can be recast into a nonconvex optimization. In order to efficiently solve it, we propose two convex relaxations, one deterministic and one stochastic. As we illustrate experimentally, these relaxations achieve over 83 percent and 86 percent success rates, respectively, even in the face of noisy data.     

Structured analysis of piecewise‐linear interconnected systems

This paper considers the problem of assessing the induced L₂ gain of a system composed of non‐identical interconnected piecewise‐linear subsystems, when the topology of the underlying graph is arbitrary. Blending tools inspired by dissipativity theory and the S‐procedure, it presents sufficient conditions in the form of a set of finite‐dimensional linear matrix inequalities which are coupled in a way that reflects the spatial structure of the system under analysis. Results are presented comparing the efficacy of the new conditions to similar conditions for an equivalent global piecewise‐linear system. Copyright © 2007 John Wiley & Sons, Ltd.     

Assessment of Eurocode-like design equations for the shear capacity of FRP RC members

Fibre reinforced polymer (FRP) bars represent an interesting alternative to conventional steel as internal reinforcement of reinforced concrete (RC) members where some properties such as durability, magnetic transparency, insulation, are of primary concern. The present paper focuses on the assessment of Eurocode-like design equations for the evaluation of the shear strength of FRP RC members, as proposed by the guidelines of the Italian Research Council CNR-DT 203 [CNR-DT 203/2006. Guide for the design and construction of concrete structures reinforced with fiber-reinforced polymer bars. National Research Council, Rome, Italy; 2006]. Both the concrete and the FRP stirrups contributions to shear are taken into account: the new equations derived with reference to Eurocode equations for shear of steel RC members are verified through comparison with the equations given by ACI, CSA and JSCE guidelines, considering a large database of members with and without shear reinforcement failed in shear.