Charles A. Desoer

Automated vehicle control developments in the PATH program

The accomplishments to date on the development of automatic vehicle control technology in the Program on Advanced Technology for the Highway (PATH) at the University of California, Berkeley, are summarized. The basic principles and assumptions underlying the PATH work are identified, and the work on automating vehicle lateral (steering) and longitudinal (spacing and speed) control is explained. For both lateral and longitudinal control, the modeling of plant dynamics is described, and the development of the additional subsystems needed (communications, reference/sensor systems) and the derivation of the control laws are presented. Plans for testing on vehicles in both near and long term are discussed. >

Necessary and sufficient condition for robust stability of linear distributed feedback systems

Considering linear time-invariant distributed feedback systems, a necessary and sufficient condition for robust stability is derived with respect to plant perturbations belonging to a specified ball. The conclusion is shown to exhibit design limitations imposed by plant uncertainties.

Multivariable feedback systems

1. On the Advantages of Feedback.- 1.1. Introduction.- 1.2. Singular Value Decomposition of a Matrix.- 1.3. Large Loop Gain.- 2. Matrix Fraction Description of Transfer Functions.- 2.1. Introduction.- 2.2. Polynomials, Euclidean Rings, and Modules.- 2.3. Polynomial Matrices.- 2.3.1. Divisors, Coprimeness, Rank.- 2.3.2. Elementary Operations on Polynomial Matrices.- 2.3.3. Elementary Operations and Differential Equations.- 2.3.4. Standard Forms: Hermite and Smith Forms.- 2.3.5. The Solution Space of D(p) ?(t) = 9 t ? 0.- 2.3.6. Greatest Common Divisor Extraction.- 2.4. Matrix Fraction Descriptions of Rational Transfer Function Matrices.- 2.4.1. Coprime Fractions.- 2.4.2. Smith-Mcmillan Form Relation to Coprime Fractions.- 2.4.3. Proper Transfer Function Matrices.- 2.4.4. Poles and Zeros.- 2.4.5. Dynamical Interpretation of Poles and Zeros.- 2.5. Realization and Polynomial Matrix Fractions.- 3. Polynomial Matrix System Descriptions and Related Transfer Functions.- 3.1. Introduction.- 3.2. Dynamics of a PMD Redundancy.- 3.2.1. Dynamics of a PMD.- 3.2.2. Reachability of PDMs.- 3.2.3. Observability of PMDs.- 3.2.4. Minimality, Hidden Modes, Poles, and Zeros.- 3.3. Well-Formed and Exponentially Stable PMDs.- 3.3.1. Well-Formed PMDs.- 3.3.2. Exponentially Stable PMDs 121 3.4. Transfer Functions: Right-Left Fractions Internally Proper Fractions.- 4. Interconnected Systems.- 4.1. Introduction.- 4.2. Exponential Stability of an Interconnection of Subsystems.- 4.3. Feedback System Exponential Stability.- 4.4. Special Properties of Feedback Systems.- 5. Single-Input Single-Output Systems.- 5.1. Introduction.- 5.2. Problem Statement and Analysis.- 5.3. Design.- 6. The Closed-Loop Eigenvalue Placement Problem.- 6.1. Introduction.- 6.2. The Compensator Problem.- 7. Asymptotic Tracking.- 7.1. Introduction.- 7.2. Theory of Asymptotic Tracking.- 7.3. The Tracking Compensator Problem.- 8. Design with Stable Plants.- 8.1. Introduction.- 8.2. Q-Parametrization Design Properties.- 8.3. Q-Design Algorithm for Decoupling by Feedback.- 8.4. Two-Step Compensation Theorem for Unstable Plants.- Epilogue.- Appendices.- A. Rings and Fields.- B. Matrices with Elements in a Commutative Ring IK.- C. Division of a Polynomial Vector on the Left by a Polynomial Matrix.- References.- Symbols.

An algebra of transfer functions for distributed linear time-invariant systems

A quotient algebra of transfer functions of distributed linear time-invariant subsystems is proposed; this algebra is a generalization of the algebra of proper rational functions. Its main virtue is that it allows the algebraic manipulation of distributed systems within the algebra. Series, parallel, and, under some regularity conditions, feedback interconnection of transfer functions in the algebra remain in the algebra. The relation of our algebra to the algebras proposed by Morse, Dewilde, and Kamen is discussed and the algebras are compared. Finally, applications of the algebra are indicated.

Slowly varying system ẋ = A(t)x

A limiting case of great importance in engineering is that of slowly varying parameters. For systems described by \dot{x} = A(t)x , one would intuitively expect that if, for each t , the frozen system is stable, then the time-varying system should also be stable. Provided A(t) is small enough, Rosenbrock has shown that this is the case [1]. Rosenbrock used a continuity argument [1, p. 75]. In this correspondence explicit bounds and slightly sharper results are obtained. Finally, it is pointed out that these results are useful in the study of the exact behavior of non-linear lumped systems with slowly varying operating points.

Longitudinal control of a platoon of vehicles with no communication of lead vehicle information: a system level study

The paper considers the problem of longitudinal control of a platoon of automotive vehicles on a straight lane of a highway and proposes control laws in the event of loss of communication between the lead vehicle and the other vehicles in the platoon. After discussing the main design objectives for the proposed control laws, the authors formulate these objectives as a constrained optimization problem. By solving this optimization problem, they obtain longitudinal control laws for a platoon of vehicles which does not use any communication from the lead vehicle to the other vehicles in the platoon. Comparison between these control laws and the control laws which use such a communication link to transmit lead-vehicle information to the other vehicles in a platoon shows that, in the case of loss of communication between the lead vehicle and the other vehicles, the performance of the longitudinal control laws degrades; however, this degradation is not catastrophic. >

Tracking and disturbance rejection of MIMO nonlinear systems with PI controller

We study tracking and disturbance rejection of a class of MIMO nonlinear systems with linear proportional plus integral (PI) compensator. Roughly speaking, we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady-state I/O map, then a simple PI compensator can be used to yield a stable unity-feedback closed-loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors.

An elementary proof of Kharitonov's stability theorem with extensions

Gives an elementary proof of Kharitonovs theorem using simple complex plane geometry without invoking the Hermite-Bieler theorem. Kharitonovs theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval. The result states that the whole class is Hurwitz if and only if four special, well-defined polynomials are Hurwitz. The paper also gives elementary proofs of two previously known extensions: for polynomials of degree less than six, the requirement is reduced to fewer than four polynomials; and the theorem is generalized to polynomials with complex coefficients. >

Foundations of feedback theory for nonlinear dynamical systems

We study the fundamental properties of feedback for nonlinear, time-varying, multi-input muldt-output, distributed systems. The classical Black formula is generalized to the nonlinear case. Achievable advantages and limitations of feedback in nonlinear dynamical systems are classified and studied in five categories: desensitization, disturbance attenuation, linearizing effect, asymptotic tracking and disturbance rejection, stabilization. Conditions under which feedback is beneficial for nonlinear dynamical systems are derived. Our results show that if the appropriate linearized inverse return difference operator is small, then the nonlinear feedback system has advantages over the open-loop system. Several examples are proyided to illustrate the results.

Stability of dithered non-linear systems with backlash or hysteresis

We study the effect of dither on the non-linear element of a single-input single-outout feedback system. We consider non-linearities with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the non-linearity. The non-linearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the non-linearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system