Data-Driven Control of Linear Time-Varying Systems

An identification-free control design strategy for discrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under state feedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collected offline. This data-driven system representation is used to classify control laws yielding trajectories which satisfy a certain bound and to solve the linear quadratic regulator problem - both using data-dependent linear matrix inequalities only. The results are illustrated by means of a numerical example

A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems

With the aim of designing controllers to simultaneously ensure robustness and optimality properties, the mixed H2/H∞ control problem is considered. A class of input-affine nonlinear systems is considered and the problem is formulated as a nonzero-sum differential game, similar to what has been done in the 1990s by Limebeer et al. for linear systems. A heuristic algorithm for obtaining solutions for the coupled algebraic Riccati equations which are characteristic of the linear quadratic problem is provided together with a systematic method for constructing approximate solutions for the general, nonlinear problem. A few numerical examples are provided

Approximate infinite-horizon optimal control for stochastic systems

The policy of an optimal control problem for nonlinear stochastic systems can be characterized by a second- order partial differential equation for which solutions are not readily available. In this paper we provide a systematic method for obtaining approximate solutions for the infinite-horizon optimal control problem in the stochastic framework. The method is demonstrated on an illustrative numerical example in which the control effort is not weighted, showing that the technique is able to deal with one of the most striking features of stochastic optimal control

Finite-dimensional characterisation of optimal control laws over an infinite horizon for nonlinear systems

Infinite-horizon optimal control problems for nonlinear systems are considered. Due to the nonlinear and intrinsically infinite-dimensional nature of the task, solving such optimal control problems is challenging. In this paper an exact finite-dimensional characterisation of the optimal solution over the entire horizon is proposed. This is obtained via the (static) minimisation of a suitably defined function of (projected) trajectories of the underlying Hamiltonian dynamics on a hypersphere of fixed radius. The result is achieved in the spirit of the so-called shooting methods by introducing, via simultaneous forward/backward propagation, an intermediate shooting point much closer to the origin, regardless of the actual initial state. A modified strategy allows one to determine an arbitrarily accurate approximate solution by means of standard gradient-descent algorithms over compact domains. Finally, to further increase robustness of the control law, a receding-horizon architecture is envisioned by designing a sequence of shrinking hyperspheres. These aspects are illustrated by means of a benchmark numerical simulation

Zero finding via feedback stabilisation

Two iterative algorithms for solving systems of linear and nonlinear equations are proposed. For linear problems the algorithm is based on a control theoretic approach and it is guaranteed to yield a converging sequence for any initial condition provided a solution exists. Systems of nonlinear equations are then considered and a generalised algorithm, again taking inspiration from control theory, is proposed. Local convergence is guaranteed in the nonlinear setting. Both the linear and the nonlinear algorithms are demonstrated on a series of numerical examples

Crowd-Averse Robust Mean-Field Games: Approximation via State Space Extension

We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a crosscoupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowdaverse”. Motivations for this model are analyzed and discussed in three main contexts: a stock market application, a production engineering example, and a dynamic demand management problem in power systems. For the problem in its abstract formulation, we illustrate the paradigm of robust mean-field games. Main contributions involve first the formulation of the problem as a robust mean-field game; second, the development of a new approximate solution approach based on the extension of the state space; third, a relaxation method to minimize the approximation error. Further results are provided for the scalar case, for which we establish performance bounds, and analyze stochastic stability of both the microscopic and the macroscopic dynamics

Invasive group A, C and G streptococcal disease in western Norway: virulence gene profiles, clinical features and outcomes

AbstractInvasive group A streptococcal (iGAS) disease is endemic in Norway, but data on invasive group C and group G streptococcal (iGCS/GGS) disease are lacking. We investigated the characteristics of iGAS and iGCS/GGS infections in western Norway from March 2006 to February 2009. Clinical information was retrospectively obtained from medical records. GAS and GCS/GGS isolates were emm typed and screened for the presence of 11 superantigen (SAg) genes and the gene encoding streptococcal phospholipase A2 (SlaA). GCS/GGS isolates were also subjected to PCR with primers targeting speGdys. Sixty iGAS and 50 iGCS/GGS cases were identified, corresponding to mean annual incidence rates of 5.0 per 100 000 and 4.1 per 100 000 inhabitants, respectively. Skin and soft tissue infections were the most frequent clinical manifestations of both iGAS and iGCS/GGS disease, and 14 iGAS patients (23%) developed necrotizing fasciitis. The 30-day case fatality rates of iGAS and iGCS/GGS disease were 10% and 2%, respectively. emm1, emm3 and emm28 accounted for 53% of the GAS isolates, and these types were associated with severe clinical outcome. SAg gene and SlaA profiles were conserved within most of the GAS emm types, although five profiles were obtained within isolates of emm28. stG643 was the most prevalent GCS/GGS emm type, and speGdys was identified in 73% of the GCS/GGS isolates. Neither GAS SAg genes nor SlaA were detected in GCS/GGS. Our findings indicate a considerable burden of both iGAS and iGCS/GGS disease and a high frequency of necrotizing fasciitis caused by GAS in our community

Approximate solutions for crowd-averse robust mean-field games

We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term 'crowd-averse'. For this game we first illustrate the paradigm of robust mean-field games. Second, we provide a new approximate solution approach based on the extension of the state space and prove the existence of equilibria and their stability properties

Mean-field games and two-point boundary value problems

© 2014 IEEE. A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example

emm gene diversity, superantigen gene profiles and presence of SlaA among clinical isolates of group A, C and G streptococci from western Norway

In order to investigate molecular characteristics of beta-hemolytic streptococcal isolates from western Norway, we analysed the entire emm gene sequences, obtained superantigen gene profiles and determined the prevalence of the gene encoding streptococcal phospholipase A2 (SlaA) of 165 non-invasive and 34 contemporary invasive group A, C and G streptococci (GAS, GCS and GGS). Among the 25 GAS and 26 GCS/GGS emm subtypes identified, only emm3.1 was significantly associated with invasive disease. M protein size variation within GAS and GCS/GGS emm types was frequently identified. Two non-invasive and one invasive GGS possessed emm genes that translated to truncated M proteins as a result of frameshift mutations. Results suggestive of recombinations between emm or emm-like gene segments were found in isolates of emm4 and stG485 types. One non-invasive GGS possessed speC, speG, speH, speI and smeZ, and another non-invasive GGS harboured SlaA. speA and SlaA were over-represented among invasive GAS, probably because they were associated with emm3. speGdys was identified in 83% of invasive and 63% of non-invasive GCS/GGS and correlated with certain emm subtypes. Our results indicate the invasive potential of isolates belonging to emm3, and show substantial emm gene diversity and possible lateral gene transfers in our streptococcal population