Anders Rantzer

In a previous paper, we showed how classical ideas for dynamic programming in discrete networks can be adapted to hybrid systems. The approach is based on discretization of the continuous Bellman...

u w (2007)

The servo problem for piecewise linear systems (2007)

This paper presents a linear programming (LP) algorithm for an optimal robust controller design under parametric uncertainty. This algorithm is based on the convex robust controller parameterization...

Stefan Solyom, Anders Rantzer

The servo problem for a wide class of nonlinear system is considered. A quantitative bound on system trajectories is derived. For piecewise linear systems the bound is shown to be computable in terms...

Improving Efficiency in the omputation of Piecewise (uadratie Lyapunov Functions (2007)

Mikael Johansson, Andrey Ghulchak, Anders Rantzer

In a series of papers, the authors have developed a method for analysis of piecewise linear systems. The idea is to use Lyapunov functions that are piecewise quadratic. Such Lyapunov functions can be...

Hybrid Control Laws From Convex Dynamic Programming (2007)

Robust Control under Parametric Uncertainty via Primal-Dual Convex Analysis (2007)

In a previous paper, we showed how classical ideas for dynamic programming in discrete networks can be adapted to hybrid systems. The approach is based on discretization of the continuous Bellman...

Duality In H Cone Optimization (2007)

A numerical method is proposed for optimal robust control synthesis. The method applies to the case when the coefficients of the characteristic polynomial depend linearly on the uncertain parameters....

Convex Programs for Temporal Verification of Nonlinear Dynamical Systems (2007)

Positive real cones in the space H # appear naturally in many optimization problems of control theory and signal processing. Although such problems can be solved by finite-dimensional approximations...

MTNS Problem Book (2007)

Open Problems On, Vincent D. Blondel, Alexander Megretski, Roger Brockett, Jean-michel Coron, Miroslav Krstic, ...

this paper we consider the well-known Schur problem the solution of which satisfy in addition the extremal condition (z)w(z) min ; jzj < 1 (58.1) where w(z) and min are mxm matrices and min > 0...

Primal Dual Tests for Safety and Reachability (2005)

A methodology for safety verification of continuous and hybrid systems using barrier certificates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be...

Linear Quadratic Performance Criteria for Cascade Control (2005)

A methodology for safety verification using barrier certifi- cates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and...

Gattami, Ather, Rantzer, Anders

In this paper we consider the problem of linear quadratic regulator (LQR) performance for cascade control structures of series coupled systems. The necessary and sufficient condition for the linear...

Sub-Optimal Sensor Scheduling with Error Bounds (2005)

Alriksson, Peter, Rantzer, Anders

In this paper the problem of sub-optimal sensor schedulingwith a guaranteed distance to optimality is considered. Optimal in thesense that the sequence that minimizes the estimation error...

Robust stability analysis of linear systems with time-varying delays (2005)

Kao, Chung-Yao, Rantzer, Anders

Robust stability of linear systems in presence of bounded uncertain time-varying time delays is studied. The time delay robustness problem is treated in the Integral Quadratic Constraint framework....

On the necessity of barrier certificates (2005)

On approximate policy iteration for continuous-time systems (2005)

A methodology for safety verification of nonlinear systems using barrier certificates has been proposed recently. The condition was stated in a sufficiency form: if there exists a barrier...

Wernrud, Andreas, Rantzer, Anders

We propose a new algorithm for feedback nonlinear synthesis. The algorithm computes suboptimal solutions, with bounds on suboptimality, to the Hamilton-Jacobi-Bellman equation. For systems that are...

On Approximate Dynamic Programming in Switching Systems (2005)

Nonlinear control synthesis by convex optimization (2004)

In order to simplify computational methods based on dynamic programming, an approximative procedure based on upper and lower bounds of the optimal cost was recently introduced. The convergence...

Prajna, Stephen, Parrilo, Pablo A., Rantzer, Anders

A stability criterion for nonlinear systems, recently derived by the third author, can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be...

Nonlinear Control Synthesis by Convex Optimization (2004)

Prajna, Stephen, Parrilo, Pablo, Rantzer, Anders

A stability criterion for nonlinear systems, recently derived by thethird author, can be viewed as a dual to Lyapunov's second theorem.The criterion is stated in terms of a function which can...

Balanced truncation of linear time-varying systems (2004)

Sandberg, Henrik, Rantzer, Anders

In this paper balanced truncation of linear time-varying systems is studied in discrete and continuous time. Based on relatively basic calculations with time-varying Lyapunov equations/inequalities...

On Analysis and Synthesis of Safe Control Laws (2004)

Rantzer, Anders, Prajna, Stephen

Controller synthesis for nonlinear systems is considered with the following objective: No trajectory starting from a given set of initial states is allowed to enter into a given set of forbidden...

Synthesis of a Model-based Tire Slip Controller (2004)

Solyom, Stefan, Rantzer, Anders, Lüdemann, Jens

The Anti-lock Braking System is an important component of the steeringsystem in a modern car. In the latestgeneration of brake-by-wire systems, the performance requirementson the ABS are much higher....

A novel method for voltage stability control in power systems (2004)

Solyom, Stefan, Lincoln, Bo, Rantzer, Anders

A novel method for voltage stability control in power networks is considered. Dynamic compensation of the voltage reference is used togheter with a VIP (voltage instability predictor) based load...

l2 gain bounded adaptive control of a first order linear system (2004)

On Homogeneous Density Functions (2003)

The problem of adaptive control is considered from a perspective of l2-gain. It has recently been shown that without an a priori bound on the system parameters, there exists no single dynamic...

Density and Cost in Non-linear Control (2003)

We consider homogeneous density functions for proving almost globalattractivity of the zero equilibrium in a homogeneous system. It is shownthat the existence of such a function is guaranteed whenthe...

Rantzer, Anders, Hedlund, Sven

The duality between cost and flow is well known and carefully studiedin several scientific fields, including economics and fluid mechanics.The purpose of this paper is to show how this duality...

ABS control - A design model and control structure (2003)

Solyom, Stefan, Rantzer, Anders

The Anti-lock Braking System is an important component of acomplex steering system for the modern car. Most of ABS controllersavailable on the market are table and relay-feedback based.In the latest...

Relaxed Optimal Control of Piecewise Linear Systems (2003)

Lincoln, Bo, Rantzer, Anders

This paper applies a dynamic programming relaxation methodpreviously proposed by the authors to optimal control of piecewise linearsystems. The method gives an algorithm to find a sub-optimal...

Stability Criteria for Systems with Bounded Uncertain Time-varying Delay (2003)

Kao, Chung-Yao, Rantzer, Anders

Abstract not available

Duality between cost and density in optimal control (2003)

Rantzer, Anders, Hedlund, Sven

A theorem on duality between cost functions and density functions in optimal control is derived using the Hahn-Banach theorem. The result puts focus on convexity aspects in control synthesis and the...

Robust Control under Parametric Uncertainty via Primal-Dual Convex Analysis (2002)

Ghulchak, Andrey, Rantzer, Anders

A numerical synthesis method for optimally robust control isproposed. The method applies to the case of linear dependenceon uncertain parameters in the characteristic polynomial. Aprimal/dual pair of...

Duality in $H^infty$ Cone Optimization (2002)

Ghulchak, Andrey, Rantzer, Anders

Positive real cones in the space H$^\infty$ appear naturally in many optimization problems of control theory and signal processing. Although such problems can be solved by finite-dimensional...

Convex Dynamic Programming for Hybrid Systems (2002)

Hedlund, Sven, Rantzer, Anders

A classical linear programming approach to optimization of flow or transportation in a discrete graph is extended to hybrid systems. The problem is finite-dimensional if the state space is discrete...

Error Bounds for Balanced Truncation of Linear Time-Varying Systems (2002)

Sandberg, Henrik, Rantzer, Anders

In this paper error bounds for truncatedbalanced linear time-varying systems in discrete time are obtained.The analysis is based on direct calculations with the time-varyingobservability and...

Optimal control for systems with varying sampling rate (2002)

Schinkel, Michael, Chen, Wen-Hua, Rantzer, Anders

The paper addresses the aspects of control of real time systems with varying sampling rate. An example is given in which a stable continuous system is sampled at two different sampling rates. Two...

The servo problem for piecewise linear systems (2002)

Solyom, Stefan, Rantzer, Anders

The servo problem for a wide class of nonlinear system is considered.A quantitative bound on system trajectories is derived. For piecewise linearsystems the bound is shown to be computable in terms...

Balanced Model Reduction of Linear Time-Varying Systems (2002)

Sandberg, Henrik, Rantzer, Anders

This paper treats model reduction of linear time-varying models in continuous time. The method proposed is based on time-varying Lyapunov inequalities and balancing of Gramians. An error bound for...

Suboptimal dynamic programming with error bounds (2002)

Lincoln, Bo, Rantzer, Anders

This paper presents a method to relax Dynamic Programming. The methodmakes it possible to findsuboptimal solutions with known error bounds to hard problems.The bounds are chosen by the user, who can...

A converse theorem for density functions (2002)

A dual to Lyapunov's stability theorem (2001)

It is proved that existence of a density function is both necessaryand sufficient for almost global stability in a nonlinear system.

Optimizing linear system switching (2001)

Lyapunov's second theorem is a standard tool for stability analysis of ordinary differential equations. Here we introduce a theorem which can be viewed as a dual to Lyapunov's result. From existence...

Lincoln, Bo, Rantzer, Anders

This paper considers a class of control problems where there is a need to find switching-sequences between different linear systems, as well as linear control laws, to minimize some quadratic cost...

Almost global stability of phase-locked loops (2001)

Smooth blending of nonlinear controllers using density functions (2001)

Many control systems have a global dynamical behavior that in addition to a desired stable equilibrium has one or more unstable equilibria or other exceptional trajectories. Typical examples of such...

Rantzer, Anders, Ceragioli, Francesca

A new convergence criterion for nonlinear systems was recently derived by the first author. The criterion is similar to Lyapunov’s second theorem but differs in several respects. In particular, it...

Friction Analysis Based on Integral Quadratic Constraints (2001)

Hybrid Control Laws From Convex Dynamic Programming (2000)

Passivity arguments have long been used in the analysis of systems with friction. This paper proves a new set of integral quadratic constraints, which reduces the conservatism of such methods. The...

Hedlund, Sven, Rantzer, Anders

In a previous paper, we showed how classical ideas for dynamicprogramming in discrete networks can be adapted to hybrid systems. The approach is based on discretization of the continuous Bellman...

A Piecewise Quadratic Approach to Stability Analysis of Fuzzy Systems (2000)

Johansson, Mikael, Rantzer, Anders, Årzén, Karl-Erik

Abstract not available

On the dual of Lyapunov's second theorem (2000)

On convexity in stabilization of nonlinear systems (2000)

A stability criterion for nonlinear systems is presented and can be viewed as a dual to Lyapunov's second theorem. The criterion has a physical interpretation in terms of the stationary density of a...

Rantzer, Anders, Parrilo, Pablo

A stability criterion for nonlinear systems, derived by the first author (2000), can be viewed as a dual to Lyapunov's second theorem. The criterion is stated in terms of a function which can be...

Piecewise Linear Quadratic Optimal Control (2000)

Rantzer, Anders, Johansson, Mikael

The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are...

On convexity in stabilization of nonlinear systems (2000)

Anders Rantzer, Pablo A. Parrilo

Abstract A stability criterion for nonlinear systems, recently derived by the first author, can be viewed as a dual to Lyapunov’s second theorem. The criterion is stated in terms of a function...

Editors (1999)

Vincent D. Blondel, Alexander Megretski, Roger Brockett, Jean-michel Coron, Miroslav Krstic, Anders Rantzer, ...

Some of the problems appearing in this booklet will appear in a more extensive forthcoming book on open problems in systems theory. For more information about this future book, please consult the...

CDP Tool: A Matlab tool for optimal control of hybrid systems. Department of Automatic Control (1999)

Optimal control of hybrid systems (1999)

This manual describes CDP Tool, a MATLAB too1 that solves hybrid optimal con-trol problems via CDP (Convex Dynamic Programming). The manual is orga-nized as follows: Section 2 defines the problems...

Improving Efficiency in the Computation of Piecewise Quadratic Lyapunov Functions (1999)

This paper presents a method for optimal control of hybrid systems. An inequality of Bellman type is considered and every solution to this inequality gives a lower bound on the optimal value...

Mikael Johansson, Andrey Ghulchak, Anders Rantzer

In a series of papers, the authors have developed a method for analysis of piecewise linear systems. The idea is to use Lyapunov functions that are piecewise quadratic. Such Lyapunov functions can be...

Dynamic Programming Via Convex Optimization (1999)

Anders Rantzer

It has long been known that a wide class of problems in optimal control can be stated as infinite-dimensional convex optimization problems, where the Bellman equation is relaxed to inequality. In...

Optimal Control of Hybrid Systems (1999)

Robust Controller Design via Linear Programming (1999)

This paper presents a method for optimal control of hybrid systems. An inequality of Bellman type is considered and every solution to this inequality gives a lower bound on the optimal value...

Optimal control of hybrid systems (1999)

This paper presents a linear programming (LP) algorithm for an optimal robust controller design under parametric uncertainty. This algorithm is based on the convex robust controller parameterization...