A scenario approach for non-convex control design

Randomized optimization is an established tool for control design with modulated robustness. While for uncertain convex programs there exist randomized approaches with efficient sampling, this is not the case for non-convex problems. Approaches based on statistical learning theory are applicable to non-convex problems, but they usually are conservative in terms of performance and require high sample complexity to achieve the desired probabilistic guarantees. In this paper, we derive a novel scenario approach for a wide class of random non-convex programs, with a sample complexity similar to that of uncertain convex programs and with probabilistic guarantees that hold not only for the optimal solution of the scenario program, but for all feasible solutions inside a set of a-priori chosen complexity. We also address measure-theoretic issues for uncertain convex and non-convex programs. Among the family of non-convex control- design problems that can be addressed via randomization, we apply our scenario approach to randomized Model Predictive Control for chance-constrained nonlinear control-affine systems.Comment: Submitted to IEEE Transactions on Automatic Contro

A Verification-Driven Approach to Control Analysis and Tuning

This paper proposes a methodology for the analysis and tuning of controllers using control verification metrics. These metrics, which are introduced in a companion paper, measure the size of the largest uncertainty set of a given class for which the closed-loop specifications are satisfied. This framework integrates deterministic and probabilistic uncertainty models into a setting that enables the deformation of sets in the parameter space, the control design space, and in the union of these two spaces. In regard to control analysis, we propose strategies that enable bounding regions of the design space where the specifications are satisfied by all the closed-loop systems associated with a prescribed uncertainty set. When this is unfeasible, we bound regions where the probability of satisfying the requirements exceeds a prescribed value. In regard to control tuning, we propose strategies for the improvement of the robust characteristics of a baseline controller. Some of these strategies use multi-point approximations to the control verification metrics in order to alleviate the numerical burden of solving a min-max problem. Since this methodology targets non-linear systems having an arbitrary, possibly implicit, functional dependency on the uncertain parameters and for which high-fidelity simulations are available, they are applicable to realistic engineering problems.

Figures of Merit for Control Verification

This paper proposes a methodology for evaluating a controller's ability to satisfy a set of closed-loop specifications when the plant has an arbitrary functional dependency on uncertain parameters. Control verification metrics applicable to deterministic and probabilistic uncertainty models are proposed. These metrics, which result from sizing the largest uncertainty set of a given class for which the specifications are satisfied, enable systematic assessment of competing control alternatives regardless of the methods used to derive them. A particularly attractive feature of the tools derived is that their efficiency and accuracy do not depend on the robustness of the controller. This is in sharp contrast to Monte Carlo based methods where the number of simulations required to accurately approximate the failure probability grows exponentially with its closeness to zero. This framework allows for the integration of complex, high-fidelity simulations of the integrated system and only requires standard optimization algorithms for its implementation

A nonlinear approach to the control of a disc-shaped aircraft

International audienceThis paper describes a new control approach for scale-model airplanes. The proposed control solution is primarily geared towards drones whose lift surfaces can be approximated by a disc-shaped wing. Designed and analysed on the basis of a specific model of aerodynamic forces acting on the aircraft, it departs from other solutions in its capacity to handle important and rapidly changing attack angles within a large flight envelope. Simulation results illustrate its robust performance

A Computational Framework to Control Verification and Robustness Analysis

This paper presents a methodology for evaluating the robustness of a controller based on its ability to satisfy the design requirements. The framework proposed is generic since it allows for high-fidelity models, arbitrary control structures and arbitrary functional dependencies between the requirements and the uncertain parameters. The cornerstone of this contribution is the ability to bound the region of the uncertain parameter space where the degradation in closed-loop performance remains acceptable. The size of this bounding set, whose geometry can be prescribed according to deterministic or probabilistic uncertainty models, is a measure of robustness. The robustness metrics proposed herein are the parametric safety margin, the reliability index, the failure probability and upper bounds to this probability. The performance observed at the control verification setting, where the assumptions and approximations used for control design may no longer hold, will fully determine the proposed control assessment

Modeling and Analysis of Multiple Engine Aircraft Configurations for Fault Tolerant Control

A formal framework is presented that allows for the analysis of the potential for using engine thrust control for aircraft actuator failure accommodation. Three sets of parameters have been identified as critical: number of engines and their position, engine thrust and throttle dynamics, and type and severity of the actuator failure. A mathematical model was developed that allows for the determination of the values of some of the parameters when the others are imposed such as determining the thrust control authority when the engine locations and Euler angles are known. Additionally, the engine locations can be determined when the thrust control authority and engine Euler angles are known and the engine Euler angles can be determined when the engine locations and thrust control authority are known. A MATLAB/Simulink simulation environment was built around a model of a large transport that can accommodate up to ten engines at different locations. A fuzzy logic controller was designed and employed for failure accommodation. The fuzzy logic controller utilizes the pilot lateral, longitudinal, and directional commands as well as the aircraft\u27s pitch attitude, roll attitude, yaw attitude and respective angular rates as the inputs to the system and provides throttle commands for each engine based on its location with respect to the aircraft\u27s center of mass. Failures of varying severity on the rudder, left or right aileron, and left or right elevator were implemented. The controller was capable of accommodating an extremely severe aileron failure and moderately severe rudder failure without additional pilot input. The controller was capable of mitigating some of the pilot command required for a moderate elevator failure. The simulation environment was used to verify the analytical results and to demonstrate the fault tolerant capabilities of multiple engine configurations. It proved to be a flexible and efficient tool for analysis and control system development

Dynamics and Performance of Tailless Micro Aerial Vehicle with Flexible Articulated Wings

The purpose of this paper is to analyze and discuss the performance and stability of a tailless micro aerial vehicle with flexible articulated wings. The dihedral angles can be varied symmetrically on both wings to control the aircraft speed independently of the angle of attack and flight-path angle, while an asymmetric dihedral setting can be used to control yaw in the absence of a vertical tail.Anonlinear aero-elastic model is derived, and it is used to study the steady-state performance and flight stability of the micro aerial vehicle. The concept of the effective dihedral is introduced, which allows for a unified treatment of rigid and flexible wing aircraft. It also identifies the amount of elasticity that is necessary to obtain tangible performance benefits over a rigid wing. The feasibility of using axial tension to stiffen the wing is discussed, and, at least in the context of a linear model, it is shown that adding axial tension is effective but undesirable. The turning performance of an micro aerial vehicle with flexible wings is compared to an otherwise identical micro aerial vehicle with rigid wings. The wing dihedral alone can be varied asymmetrically to perform rapid turns and regulate sideslip. The maximum attainable turn rate for a given elevator setting, however, does not increase unless antisymmetric wing twisting is employed

Nonlinear Flight Control Design Using Backstepping Methodology

The subject of nonlinear flight control design using backstepping control methodology is investigated in the dissertation research presented here. Control design methods based on nonlinear models of the dynamic system provide higher utility and versatility because the design model more closely matches the physical system behavior. Obtaining requisite model fidelity is only half of the overall design process, however. Design of the nonlinear control loops can lessen the effects of nonlinearity, or even exploit nonlinearity, to achieve higher levels of closed-loop stability, performance, and robustness. The goal of the research is to improve control quality for a general class of strict-feedback dynamic systems and provide flight control architectures to augment the aircraft motion. The research is divided into two parts: theoretical control development for the strict-feedback form of nonlinear dynamic systems and application of the proposed theory for nonlinear flight dynamics. In the first part, the research is built on two components: transforming the nonlinear dynamic model to a canonical strict-feedback form and then applying backstepping control theory to the canonical model. The research considers a process to determine when this transformation is possible, and when it is possible, a systematic process to transfer the model is also considered when practical. When this is not the case, certain modeling assumptions are explored to facilitate the transformation. After achieving the canonical form, a systematic design procedure for formulating a backstepping control law is explored in the research. Starting with the simplest subsystem and ending with the full system, pseudo control concepts based on Lyapunov control functions are used to control each successive subsystem. Typically each pseudo control must be solved from a nonlinear algebraic equation. At the end of this process, the physical control input must be re-expressed in terms of the physical states by eliminating the pseudo control transformations. In the second part, the research focuses on nonlinear control design for flight dynamics of aircraft motion. Some assumptions on aerodynamics of the aircraft are addressed to transform full nonlinear flight dynamics into the canonical strict-feedback form. The assumptions are also analyzed, validated, and compared to show the advantages and disadvantages of the design models. With the achieved models, investigation focuses on formulating the backstepping control laws and provides an advanced control algorithm for nonlinear flight dynamics of the aircraft. Experimental and simulation studies are successfully implemented to validate the proposed control method. Advancement of nonlinear backstepping control theory and its application to nonlinear flight control are achieved in the dissertation research