Design of an LMI-based Polytopic LQR Cruise Controller for an Autonomous Vehicle towards Riding Comfort

In this paper, we present an LMI-based approach for comfort-oriented cruise control of an autonomous vehicle. First, vehicle longitudinal dynamics and a corresponding parameter-dependent state-space representation are explained and discussed. An LMI-based polytopic LQR controller is then designed for the vehicle speed to track the reference value in the presence of noise and disturbances, where the scheduling parameters are functions of the vehicle mass and the speed itself. An appropriate disturbance force compensation term is also included in the designed controller to provide a smoother response. Then we detail how the reference speed is calculated online, using polynomial functions of the given desired comfort level (quantified by the vertical acceleration absorbed by the human body) and of the road type characterized by road roughness. Finally, time-domain simulations illustrate the method’s effectiveness

Real-time Damper Force Estimation for Automotive Suspension: A Generalized H2/LPV Approach

The real-time knowledge of the damper force is of paramount importance in controlling and diagnosing automotive suspension systems. This study presents a generalized H2/LPV observer for damper force estimation of a semi-active electro-rheological (ER) suspension system. First, an extended quarter-car model augmented with the nonlinear and dynamical model of the semi-active suspension system is written into the quasi-LPV formulation. Then, the damper force estimation method is developed through a generalized H2/LPV observer whose objective is to handle the impact of unknown road disturbances and sensor noise on the estimation errors of the state variables thanks to the H2 norm. The measured sprung and unsprung mass accelerations of the quarter-car system are used as inputs for the observer. The proposed approach is simulated with validated model of the 1/5-scaled real vehicle testbed of GIPSA-lab. Simulation results show the performance of the estimation method against unknown disturbances, emphasizing the effectiveness of the damper force estimation in real time

Safety and efficacy of fluoxetine on functional outcome after acute stroke (AFFINITY): a randomised, double-blind, placebo-controlled trial

Background Trials of fluoxetine for recovery after stroke report conflicting results. The Assessment oF FluoxetINe In sTroke recoverY (AFFINITY) trial aimed to show if daily oral fluoxetine for 6 months after stroke improves functional outcome in an ethnically diverse population. Methods AFFINITY was a randomised, parallel-group, double-blind, placebo-controlled trial done in 43 hospital stroke units in Australia (n=29), New Zealand (four), and Vietnam (ten). Eligible patients were adults (aged ≥18 years) with a clinical diagnosis of acute stroke in the previous 2–15 days, brain imaging consistent with ischaemic or haemorrhagic stroke, and a persisting neurological deficit that produced a modified Rankin Scale (mRS) score of 1 or more. Patients were randomly assigned 1:1 via a web-based system using a minimisation algorithm to once daily, oral fluoxetine 20 mg capsules or matching placebo for 6 months. Patients, carers, investigators, and outcome assessors were masked to the treatment allocation. The primary outcome was functional status, measured by the mRS, at 6 months. The primary analysis was an ordinal logistic regression of the mRS at 6 months, adjusted for minimisation variables. Primary and safety analyses were done according to the patient's treatment allocation. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12611000774921. Findings Between Jan 11, 2013, and June 30, 2019, 1280 patients were recruited in Australia (n=532), New Zealand (n=42), and Vietnam (n=706), of whom 642 were randomly assigned to fluoxetine and 638 were randomly assigned to placebo. Mean duration of trial treatment was 167 days (SD 48·1). At 6 months, mRS data were available in 624 (97%) patients in the fluoxetine group and 632 (99%) in the placebo group. The distribution of mRS categories was similar in the fluoxetine and placebo groups (adjusted common odds ratio 0·94, 95% CI 0·76–1·15; p=0·53). Compared with patients in the placebo group, patients in the fluoxetine group had more falls (20 [3%] vs seven [1%]; p=0·018), bone fractures (19 [3%] vs six [1%]; p=0·014), and epileptic seizures (ten [2%] vs two [<1%]; p=0·038) at 6 months. Interpretation Oral fluoxetine 20 mg daily for 6 months after acute stroke did not improve functional outcome and increased the risk of falls, bone fractures, and epileptic seizures. These results do not support the use of fluoxetine to improve functional outcome after stroke

Integrated Comfort-Adaptive Cruise and Semi-Active Suspension Control for an Autonomous Vehicle: An LPV Approach

This paper presents an integrated linear parameter-varying (LPV) control approach of an autonomous vehicle with an objective to guarantee driving comfort, consisting of cruise and semi-active suspension control. First, the vehicle longitudinal and vertical dynamics (equipped with a semi-active suspension system) are presented and written into LPV state-space representations. The reference speed is calculated online from the estimated road type and the desired comfort level (characterized by the frequency weighted vertical acceleration defined in the ISO 2631 norm) using precomputed polynomial functions. Then, concerning cruise control, an LPV H2 controller using a linear matrix inequality (LMI) based polytopic approach combined with the compensation of the estimated disturbance forces is developed to track the comfort-oriented reference speed. To further enhance passengers’ comfort, a decentralized LPV H2 controller for the semi-active suspension system is proposed, minimizing the effect of the road profile variations. The interaction with cruise control is achieved by the vehicle’s actual speed being a scheduling parameter for suspension control. To assess the strategy’s performance, simulations are conducted using a realistic nonlinear vehicle model validated from experimental data. The simulation results demonstrate the proposed approach’s capability to improve driving comfort

Kalman-like Observer for Hybrid Systems with Linear Maps and Known Jump Times (Full Version)

International audienceWe propose a hybrid Kalman-like observer for general hybrid systems with linear (time-varying) dynamics and output maps, where the solutions' jump times are exactly known. After defining a hybrid observability Gramian and the corresponding hybrid uniform complete observability, we show that the estimate provided by this observer converges asymptotically to the system solution if this observability holds together with some boundedness and invertibility conditions along the considered system solution. Then, under additional uniformity and strictness of the forgetting factors, we show exponential stability of the estimation error with an arbitrarily fast rate. The robust stability of this error against input disturbances and measurement noise is also studied. The results are illustrated on several benchmark examples, including switched systems, hybrid systems with discontinuous solutions, and continuoustime systems with multi-rate sporadic outputs

Arbitrarily Fast Robust KKL Observer for Nonlinear Time-varying Discrete Systems

Submitted to IEEE Transactions on Automatic ControlThis work presents the Kazantzis-Kravaris/Luenberger (KKL) observer design for nonlinear time-varying discrete systems. We first give sufficient results on the existence of a sequence of functions T_k transforming the given system dynamics into an exponentially stable filter of the output in some other target coordinates, where an observer is directly designed. Then, we prove that under uniform Lipschitz backward distinguishability, the maps T_k become uniformly Lipschitz injective after a certain time, if the target dynamics is pushed sufficiently fast. This leads to an arbitrarily fast discrete observer, which exhibits similarities with the famous high-gain observer for continuous-time systems. Input-to-state stability of the estimation error with respect to uncertainties, input disturbances, and measurement noise is then shown. Next, under the milder backward distinguishability, we show the injectivity of the maps T_k after a certain time for a generic choice of the target filter dynamics. Examples including a discretized permanent magnet synchronous motor (PMSM) illustrate the proposed observer

A Unified KKL Interval Observer for Nonlinear Discrete-time Systems

6 pages, 2 figuresThis work proposes an interval observer design for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm. Our design extends to generic nonlinear systems without any assumption on the structure of its dynamics and output maps. Relying on a transformation putting the system into a target LTI form where an interval observer can be directly designed, we then propose a method to reconstruct the bounds in the original coordinates using the bounds in the target coordinates, thanks to the Lipschitz injectivity of this transformation achieved under Lipschitz distinguishability when the target dynamics have a high enough dimension and are pushed sufficiently fast. An academic example serves to illustrate our methods

Observer Design for Hybrid Systems with Linear Maps and Known Jump Times

International audienceThis chapter unifies and develops recent developments in observer design for hybrid systems with linear dynamics and output maps, whose jump times are known. We define and analyze the (pre-)asymptotic detectability and uniform complete observability of this class of systems, then present two different routes for observer design. The first one relies on a synchronized Kalman-like observer that gathers observability from both flows and jumps. The second one consists in decomposing the state into parts with different observability properties and coupling observers estimating each of these parts, possibly exploiting an extra fictitious measurement coming from the combination of flows and jumps. These observers are based on a Linear Matrix Inequality (LMI) or the Kazantzis-Kravaris/Luenberger (KKL) paradigm. A comparison of these methods is presented in a table at the end

Non Linear Parameter Varying Observer based on Descriptor Modeling for Damper Fault Estimation

International audienceThis paper proposes an H∞ Non Linear Parameter Varying (NLPV) observer for fault estimation in semi-active Electro-Rheological (ER) suspensions. The damper fault (a loss-of-efficiency factor) is modeled as a lost force of unknown/free dynamics to be estimated. Thanks to the parameter-dependent descriptor-form system modeling, there is no assumption made on the fault dynamics, thus making this method applicable to all considered types of damper faults. The nonlinearity in the damper model is bounded by its Lipschitz property, while the road disturbance and the measurement noise are handled using the H∞ condition. The observer is parameterized and then designed by solving Linear Matrix Inequalities (LMIs) and is implemented in a polytopic gain scheduling approach. Synthesis results including Bode plots and simulations illustrate the method in both the frequency and the time domains