Ilan Rusnak

Online identification and control of linearized aircraft dynamics

An approach for online identification and control that requires weaker excitation than the existing approaches based on least-squares schemes and closed-loop systems is examined. It uses multiple-objective optimization theory to resolve the conflict between identification and controller performance as they compete for the only available resource, the inputs to the aircraft. The approach is applied to a longitudinal model of a representative linearized high-performance aircraft model. Simulation results compare the final controller with a conventional gain-scheduled pitch command augmentation system. It is demonstrated that by allowing some control input to be given to the identification process, the controllers overall performance is improved. >

Multiple objective optimization approach to adaptive and learning control

This paper formulates a new approach to the classical learning/adaptive control. problem. Our approach is based on two key observations: (1( the inherent conflict between control and identification as they compete for the only available resource, namely the input to the plant; (2) when designing and optimizing the performance of a control system the current task, as well as the repertoire of other typical future tasks which the system may encounter during its life time, should be considered. Our approach is formulated for a general nonlinear time-varying plant; thus, unlike existing adaptive control theory, the theory for a linear time-invariant system evolves as a special case of the general case. The design for the full lifetime of the system creates a methodology that specifies what current actions should be taken in addition to the tracking of the current reference trajectory, at the expense of some performance degradation in the current task, so as to improve the performance of future tasks: this is ...

State Observability and Parameters Identifiability of Stochastic Linear Systems

A new representation of stochastic linear time-invariant systems is presented. This representation generalizes in a rigorous way the concept of observability to parameters identifiability. The state of the augmented system is a combination of the state of the original system and the unknown parameters. It is shown that simultaneous state observability and parameters identifiability of linear time-invariant system is an observability problem of an augmented linear time-variant system. It is shown that the well known results derived by Least Squares(LS) algorithms evolve as a special case of the new representation. The representation yields necessary and sufficient conditions on the simultaneous state observability and parameters identifiability. These conditions apply to estimation in open and closed loop without further restrictions. Simulation results demonstrate the performance of estimation with this new approach.

Simultaneous State Observability and Parameters Identifiability of Discrete Stochastic Linear Systems

A new representation of discrete stochastic linear time-invariant systems is presented. This representation generalizes in a rigorous way the concept of observability to parameters identifiability. The state of the augmented system is a combination of the state of the orginal system and the unknown parameters. It is shown that simultaneous state observability and parameters identifiability of linear time-invariant system is an observability problem of an augmented linear time-variant system. It is shown that the well known results derived by Least Squares(LS) algorithms evolve as a special case of the new representation. The representation yields necessary and sufficient conditions on the simultaneous state observability and parameters identifiability. Sufficient conditions derived from the necessary and sufficient conditions are weaker than the well known persistent excitation conditions in the existing least squares schemes. These conditions apply to estimation in open and closed loop without further restrictions. This reestablishes the well known results for identification in closed loop. The observability analysis enables generalization of similar results for nonlinear time-varying feedback. Simulation results demonstrate the performance of estimation with this new approach.

Control for Unstable Non-Minimum Phase Uncertain Dynamic Vehicle

A control algorithm for control of linear uncertain systems is presented. This algorithm is applied to the control of an unstable nonminimum phase uncertain dynamic vehicle. The algorithm is based on the state and parameters observability canonical (SPOC) form and a certainty equivalence pole placement controller. The algorithm provides single controller for the problem of the uncertain dynamic vehicle that approaches the performance of a controller designed for perfectly known parameters within the whole range of the plants parameters uncertainty. The algorithm is globally bounded input bounded output stable and needs only the knowledge of the order of the plant. The algorithm is presented and its performance is demonstrated by simulations.New control algorithm for linear uncertain systems is presented. This algorithm is applied to the control of an unstable nonminimum phase uncertain dynamic vehicle. The algorithm is based the on the state and parameters observability canonical form and certainty equivalence pole placement controller. The algorithm provides single controller for the problem of the uncertain dynamic vehicle that approaches the performance of a controller designed for perfectly known parameters within the whole range of the plants uncertainty. The algorithm is globally bibo stable and needs only the knowledge of the order of the plant. The algorithm is presented and its performance is demonstrated by simulations.

Control of Stochastic Linear Uncertain Systems by Multiple Objective Optimization

This paper applies a new approach to the classical adaptive control problem. The approach is based on the inherent conflict between control and identification as they are competing for the only available resource, namely the input to the plant. The conflicting objective, namely, tracking vs. identification is most naturally posed and partially solved in the domain of Multiple Objective Optimization Theory. The control objective here is minimization of a quadratic criterion. The identification criterion is maximization of the Fisher information matrix. The Multiple Objective criterion is the simultaneous minimization of the quadratic criterion and maximization of the information matrix.

Generalizing the Certainty Equivalence Principle and Separation Theorems Beyond the Usual Heuristics

In the existing literature the certainty equivalence principle is often used as an accepted heuristic. The certainty equivalence principle allows one replace exact knowledge of the state by an estimate while preserving stability and performance. Separation theorems specify when the design of the controller with full state feedback is independent of the design of the state observer. The purpose of this paper is to emphasize that there is no need for the use of heuristics in applying the certainty equivalence principle and the separation principle in many control applications. Instead, this paper suggests using existing theorems that state when the certainty equivalence principle and separation theorems are applicable in the stabilization problem for a given system and outlines an approach for extending and refining these results.

Optimal control of input constrained linear systems

Explicit, closed-form formulas of optimal and suboptimal control on finite time interval for stochastic, linear, input-constrained systems are derived. The formulas are given in terms of the state transfer matrix of the system, the input constraint, weights of a quadratic criterion and noise variance. For a general system, only implicit solutions can be derived. However, for systems with positive impulse response, an explicit closed-form solution is derived. The optimal control in this case is the control for an unconstrained system with limiting on the input. The limiting function is the random-input describing function of the saturation function.<<ETX>>

Advanced Guidance Laws for Acceleration Constrained Missile, Randomly Maneuvering Target and Noisy Measurements

An explicit, closed form formulae of advanced guidance laws for a linear, time-invariant, acceleration-constrained arbitrary-order missile, and a linear, time-invariant, arbitrary-order, randomly maneuvering target with noisy position measurements are derived. Two approaches are presented. The first approach derives the optimal guidance law for a quadratic objective. The solution is the guidance law for deterministic system with limiting on the commanded acceleration applied on the estimated state. The second approach is based on the idea of applying the average of the input that would have been applied to the plant if the noises were known. The formulas of the different guidance laws are given in terms of the transfer function of the missile and acceleration constraint, the shaping filter of the maneuver of the target, responses to initial conditions, error variance matrix of the estimated state and weights in the criterion. It is demonstrated by simulations that although the optimal guidance law has improved performance in terms of the miss distance, the suboptimal average input guidance law consumes less energy.

Discrete Advanced Guidance for High Order Acceleration Constrained Missile and Maneuvering Target

An explicit closed form formula of a discrete guidance law for a linear, time-invariant, high-order and acceleration-constrained missile is presented. The formula is given in terms of the missile transfer function and acceleration constraint, and responses to initial conditions.An explicit, closed form formula of discrete advanced guidance law for a linear, time-invariant, high-order and acceleration-constrained missile and a linear, time-invariant arbitrary-order, maneuvering target is derived. The formula is given in terms of the missiles transfer function and acceleration constraint, the shaping filter of the target and responses to initial conditions. Optimal full state feedback guidance law is synthesized and compared to a first order approximation for minimum and non-minimum phase missile. Simulation of a third order missile model shows the relative gain from using the full state guidance law for several values of the missile time response and acceleration constraint.