Gary J. Balas

Decentralized receding horizon control for large scale dynamically decoupled systems

We present a detailed study on the design of decentralized receding horizon control (RHC) schemes for decoupled systems. We formulate an optimal control problem for a set of dynamically decoupled systems where the cost function and constraints couple the dynamical behavior of the systems. The coupling is described through a graph where each system is a node, and cost and constraints of the optimization problem associated with each node are only function of its state and the states of its neighbors. The complexity of the problem is addressed by breaking a centralized RHC controller into distinct RHC controllers of smaller sizes. Each RHC controller is associated with a different node and computes the local control inputs based only on the states of the node and of its neighbors. We analyze the properties of the proposed scheme and introduce sufficient stability conditions based on prediction errors. Finally, we focus on linear systems and show how to recast the stability conditions into a set of matrix semi-definiteness tests.

Road adaptive active suspension design using linear parameter-varying gain-scheduling

This paper presents a novel approach to the design of road adaptive active suspensions via a combination of linear parameter-varying control and nonlinear backstepping techniques. Two levels of adaptation are considered: the lower level control design shapes the nonlinear characteristics of the vehicle suspension as a function road conditions, while the higher level design involves adaptive switching between these different nonlinear characteristics, based on the road conditions. A quarter car suspension model with a nonlinear dynamic model of the hydraulic actuator is employed. The suspension deflection, car body acceleration, hydraulic pressure drop, and spool valve displacement are used as feedback signals. Nonlinear simulations show that these adaptive suspension controllers provide superior passenger comfort over the whole range of road conditions.

Development of Linear-Parameter-Varying Models for Aircraft

This paper presents a comparative study of three linear-parameter-varying (LPV) modeling approaches and their application to the longitudinal motion of a Boeing 747 series 100/200. The three approaches used to obtain the quasi-LPV models are Jacobian linearization, state transformation, and function substitution. Development of linear parameter varying models are a key step in applying LPV control synthesis. The models are obtained for the up-and-away flight envelope of the Boeing 747-100/200. Comparisons of the three models in terms of their advantages, drawbacks, and modeling difficulty are presented. Open-loop time responses show the three quasi-LPV models matching the behavior of the nonlinear model when in the trim region. Differences between the models are more apparent as the response of the aircraft deviates from the nominal trim conditions. ¯

Decentralized Receding Horizon Control and Coordination of Autonomous Vehicle Formations

This paper describes the application of a novel methodology for high-level control and coordination of autonomous vehicle teams and its demonstration on high-fidelity models of the organic air vehicle developed at Honeywell Laboratories. The scheme employs decentralized receding horizon controllers that reside on each vehicle to achieve coordination among team members. An appropriate graph structure describes the underlying communication topology between the vehicles. On each vehicle, information about neighbors is used to predict their behavior and plan conflict-free trajectories that maintain coordination and achieve team objectives. When feasibility of the decentralized control is lost, collision avoidance is ensured by invoking emergency maneuvers that are computed via invariant set theory.

Flight control design using robust dynamic inversion and time-scale separation

This paper presents a new method for design of flight controllers for aircraft: feedback linearization coupled with structured singular value (μ) synthesis. Feedback linearization uses natural time-scale separation between fast and slow variables. The linear μ controller enhances robustness to parameter variations and requires no scheduling with flight condition. This methodology is applied to an angle-of-attack command system for longitudinal control of a high performance aircraft. Nonlinear simulations demonstrate that the controller satisfies handling quality requirements, provides good tracking of pilot inputs, and exhibits excellent robustness over a wide range of angles-of-attack and Mach numbers.

Robust Dynamic Inversion for Control of Highly Maneuverable Aircraft

This paper presents a methodology for the design of flight controllers for aircraft operating over large ranges of angle of attack. The methodology is a combination of dynamic inversion and structured singular value (p) synthesis. An inner-loop controller, designed by dynamic inversion, is used to linearize the aircraft dynamics. This inner-loop controller lacks guaranteed robustness to uncertainties in the system model and the measurements; therefore, a robust, linear outer-loop controller is designed using /i synthesis. This controller minimizes the weighted HQO norm of the error between the aircraft response and the specified handling quality model while maximizing robustness to model uncertainties and sensor noise. The methodology is applied to the design of a pitch rate command system for longitudinal control of a high-performance aircraft. Nonlinear simulations demonstrate that the controller satisfies handling quality requirements, provides good tracking of pilot inputs, and exhibits excellent robustness over a wide range of angles of attack and Mach number. The linear controller requires no scheduling with flight conditions. HE objective of this paper is to present a method for design of flight controllers that provides desired handling qualities over a wide range of flight conditions with minimal scheduling. Acceptable stability and performance robustness must be maintained in the presence of unmodeled dynamics, uncertainties in the aircraft design model, and noisy sensor measurements. The aircraft considered in this paper is the NASA high angle-ofattack research vehicle (HARV), which is typical of future fighter aircraft. It is capable of flight at very high angles of attack and has thrust vectoring as well as conventional aerodynamic control surfaces.1 The unaugmented aircraft does not meet handling quality requirements and some type of augmentation is necessary. This paper considers only the longitudinal control. The controller relates pilot longitudinal stick input to the symmetric deflection of the stabilizer and the longitudinal deflection of the thrust vectoring vanes. The control design philosophy is to use an inner-loop, dynamic inversion controller and an outer-loop, linear \JL controller. The dynamic inversion controller linearizes the pitch rate dynamics of the aircraft; however, since model uncertainties prevent exact linearization, there will always be errors associated with this controller. A simple linear fractional transformation model of these errors is developed for use in design of the outer-loop /^ controller. This controller provides pitch rate following by minimizing the weighted //oo-norm of the difference between the actual aircraft pitch rate response to pilot stick inputs and the desired response to these inputs as given by a transfer function model based on standard handling quality specifications. Thus the outer-loop \Ji controller is an implicit model following design, which provides robustness to errors due to the lack of exact cancellation of the pitch rate dynamics by the dynamic inversion controller. Recently a number of papers have appeared that describe controllers for a highly maneuverable aircraft. In Refs. 2-5, application of linear multi-input/multi-output (MIMO) control design techniques to this problem were presented. In every case, excellent

Optimal, constant I/O similarity scaling for full-information and state-feedback control problems

Abstract In robust control problems, capturing all robustness and performance objectives in a single H∞ norm cost function is impossible. An alternative approach, still untilizing the H∞ norm, involves diagonal similarity scaling of certain closed loop transfer functions. The set of allowable diagonal scalings is problem dependent, and reflects assumptions about the uncertainty, and desired performance objectives. The scaling set considered here is a prescribed convex set of positive definite matrices. We consider the optimal constant scaling problem for the Full-Information H∞ control problem. The solution is obtained by transforming the original problem into a convex feasibility problem, specifically, a structured, linear matrix inequality. In special cases, solvability of the Full-Information problem is equivalent to solvability of the State-Feedback problem.

Invariant subspaces for LPV systems and their applications

The aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter-varying (LPV) systems by introducing the concept of parameter-varying invariant subspaces. For LPV systems affine in their parameters, algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems.

LPV control design for pitch-axis missile autopilots

The missile pitch-axis autopilot is designed using linear parameter-varying (LPV) control theory. The controller guarantees quadratic stability and bounded induced L/sub 2/-norm performance for the missile plant. Our approach is motivated by gain-scheduling methodology and provides a well founded and systematic procedure for high performance missile autopilot design.

Optical flow: a curve evolution approach

A novel approach for the computation of optical flow based on an L (1) type minimization is presented. It is shown that the approach has inherent advantages since it does not smooth the flow-velocity across the edges and hence preserves edge information. A numerical approach based on computation of evolving curves is proposed for computing the optical flow field. Computations are carried out on a number of real image sequences in order to illustrate the theory as well as the numerical approach.