Mrdjan J. Jankovic

Constructive Nonlinear Control

1 Introduction -- 1.1 Passivity, Optimality, and Stability -- 1.2 Feedback Passivation -- 1.3 Cascade Designs -- 1.4 Lyapunov Constructions -- 1.5 Recursive Designs -- 1.6 Book Style and Notation -- 2 Passivity Concepts as Design Tools -- 2.1 Dissipativity and Passivity -- 2.2 Interconnections of Passive Systems -- 2.3 Lyapunov Stability and Passivity -- 2.4 Feedback Passivity -- 2.5 Summary -- 2.6 Notes and References -- 3 Stability Margins and Optimality -- 3.1 Stability Margins for Linear Systems -- 3.2 Input Uncertainties -- 3.3 Optimality, Stability, and Passivity -- 3.4 Stability Margins of Optimal Systems -- 3.5 Inverse Optimal Design -- 3.6 Summary -- 3.7 Notes and References -- 4 Cascade Designs -- 4.1 Cascade Systems -- 4.2 Partial-State Feedback Designs -- 4.3 Feedback Passivation of Cascades -- 4.4 Designs for the TORA System -- 4.5 Output Peaking: an Obstacle to Global Stabilization -- 4.6 Summary -- 4.7 Notes and References -- 5 Construction of Lyapunov functions -- 5.1 Composite Lyapunov functions for cascade systems -- 5.2 Lyapunov Construction with a Cross-Term -- 5.3 Relaxed Constructions -- 5.4 Stabilization of Augmented Cascades -- 5.5 Lyapunov functions for adaptive control -- 5.6 Summary -- 5.7 Notes and references -- 6 Recursive designs -- 6.1 Backstepping -- 6.2 Forwarding -- 6.3 Interlaced Systems -- 6.4 Summary and Perspectives -- 6.5 Notes and References -- A Basic geometric concepts -- A.1 Relative Degree -- A.2 Normal Form -- A.3 The Zero Dynamics -- A.4 Right-Invertibility -- A.5 Geometric properties -- B Proofs of Theorems 3.18 and 4.35 -- B.1 Proof of Theorem 3.18 -- B.2 Proof of Theorem 4.35.

Control Lyapunov-Razumikhin functions and robust stabilization of time delay systems

Motivated by control Lyapunov functions and Razumikhin theorems on stability of time delay systems, we introduce the concept of control Lyapunov-Razumikhin functions (CLRF). The main reason for considering CLRFs is construction of robust stabilizing control laws for time delay systems. Most existing universal formulas that apply to CLFs, are not applicable to CLRFs. It turns out that the domination redesign control law applies, achieving global practical stability and, under an additional assumption, global asymptotic stability. This additional assumption is satisfied in the practically important case when the quadratic part of a CLRF is itself a CLRF for the Jacobian linearization of the system. The CLRF based domination redesign possesses robustness to input unmodeled dynamics including an infinite gain margin. While, in general, construction of CLRFs is an open problem, we show that for several classes of time delay systems a CLRF can be constructed in a systematic way.

Constructive Lyapunov control design for turbocharged diesel engines

Presents a control design method for diesel engines equipped with a variable geometry turbocharger and an exhaust gas recirculation valve. Our control objective is to regulate the air-fuel ratio and the fraction of recirculated exhaust gas to their respective set points that depend on engine operating conditions. Interactions between the two actuators and nonlinear behavior of the system make the problem difficult to handle using classical control design methods. Instead, we employ a control Lyapunov function (CLF) based nonlinear control design method because it possesses a guaranteed robustness property equivalent to gain and phase margins. The CLF is constructed using input-output linearization of a reduced order diesel engine model. The controller has been tested in simulations on the full order model as well as experimentally in the dynamometer test cell.

Constructive Lyapunov stabilization of nonlinear cascade systems

We present a global stabilization procedure for nonlinear cascade and feedforward systems which extends the existing stabilization results. Our main tool is the construction of a Lyapunov function for a class of (globally stable) uncontrolled cascade systems. This construction serves as a basis for a recursive controller design for cascade and feedforward systems. We give conditions for continuous differentiability of the Lyapunov function and the resulting control law and propose methods for their exact and approximate computation.

EGR-VGT control schemes: experimental comparison for a high-speed diesel engine

Variable-geometry turbochargers (VGTs) are employed in high-end diesel engines. These VGTs also help in controlling the trade-offs in emissions performance. Exhaust gas recirculation (EGR) is used to dilute the combustion mixture, resulting in lower peak combustion temperatures and a lower oxygen concentration and hence lower NOx emissions. In this article, we compare some of the control methodologies previously presented and some not yet presented to evaluate their benefits experimentally. We do not include any new theory. Rather we refer to other sources for the development of the controllers evaluated. We present an objective comparison of advanced control methodologies on a complex industrial problem with widespread applications. The control methodologies discussed are essentially system based, i.e., the initial controller is developed on an engine model.

TORA example: cascade- and passivity-based control designs

We consider the problem of feedback stabilization of translational oscillations by a rotational actuator (TORA) system. The main obstacle to controller design is nonlinear coupling from the rotational to the translational motion through a sinusoidal term. We present several controller designs based on the cascade and passivity paradigms.

Integrator forwarding: a new recursive nonlinear robust design

We consider the global stabilization of nonlinear systems in strict feedforward form. We show that these systems, while not feedback linearizable, can be (globally) transformed by feedback and diffeomorphism into lower-triangular form. The transformation is explicit and recursive. We employ this transformation to design a globally stabilizing controller with optimality properties and an input-to-state stability property with respect to matched uncertainties

Robust nonlinear controller for turbocharged diesel engines

This paper addresses a problem of controlling diesel engines equipped with a variable geometry turbocharger and an exhaust gas recirculation valve. The presence of two actuators and nonlinear behavior of the system makes the problem difficult to handle using classical control designs. Instead, we employ a recently developed control Lyapunov function based design method that guarantees a robustness property interpretable as gain and phase margins. The controller has been tested in simulations and experimentally in the dynamometer test cell.

Nonlinear Observer-Based Control of Load Transitions in Homogeneous Charge Compression Ignition Engines

This paper presents a model-based nonlinear feedback controller designed to regulate the crank angle at 50% fuel burned (thetasCA50) for a gasoline homogeneous charge compression ignition engine model during load transitions. The regulation of the combustion timing is based on manipulating the charge temperature through internal dilution, which is achieved by controlling the lift of a secondary opening of the exhaust valve, also known as the rebreathing lift. The nonlinear feedback controller developed is based on a positive semidefinite Lyapunov function using a simplified control model which contains only the cycle-to-cycle temperature dynamics. The nonlinear feedback controller depends on measurement of the combustion timing thetasCA50 and estimation of the temperature at intake valve closing. Closed-loop simulation of the full-order engine model shows that the nonlinear feedback controller, along with a nonlinear observer, is able to regulate the combustion timing thetasCA50 by stabilizing the temperature dynamics during load transitions. The closed-loop system with the observer-based feedback controller is shown to be robust to some classes of model uncertainty and measurement noise through simulation and an estimate of the region of attraction

Recursive predictor design for state and output feedback controllers for linear time delay systems

This paper presents a recursive method to design state and output feedback controllers for MIMO, block-feedforward linear systems with delays in the inputs, outputs, and interconnections between the blocks. The resulting controller is of predictor-type, which means that it contains finite integrals over past state and input values. The method is a generalization of the well-known model reduction approach for systems with input delay. A recursive procedure replaces delay terms with non-delay ones step by step, from the top of the cascade structure down. Controller gains are computed for the proxy system without delays, while the construction guarantees the same closed loop poles for the delay system and the proxy one. The observer is designed by applying the duality argument and the separation principle is also shown to apply.