Martin A. Sehr

Particle Model Predictive Control: Tractable Stochastic Nonlinear Output-Feedback MPC

We combine conditional state density construction with an extension of the Scenario Approach for stochastic Model Predictive Control to nonlinear systems to yield a novel particle-based formulation of stochastic nonlinear output-feedback Model Predictive Control. Conditional densities given noisy measurement data are propagated via the Particle Filter as an approximate implementation of the Bayesian Filter. This enables a particle-based representation of the conditional state density, or information state, which naturally merges with scenario generation from the current system state. This approach attempts to address the computational tractability questions of general nonlinear stochastic optimal control. The Particle Filter and the Scenario Approach are shown to be fully compatible and -- based on the time- and measurement-update stages of the Particle Filter -- incorporated into the optimization over future control sequences. A numerical example is presented and examined for the dependence of solution and computational burden on the sampling configurations of the densities, scenario generation and the optimization horizon.

Pre-filtering in gain-scheduled and robust control

We revisit the issue of gain-scheduled versus robust control with a focus on matrix inequalities. It has been established that for uncertain continuous-time linear systems that depend affinely on the uncertainty, gain-scheduled stabilizability implies robust stabilizability. That is, as far as stabilizability is concerned, using a more complex gain-scheduled controller brings no advantage. In the case of performance and discrete-time systems, counter-examples exist that show that gain-scheduling can indeed be advantageous. These proof are unfortunately not constructive, and the associated necessary and sufficient conditions are hard to verify even in low dimensions. In practice, conditions based on Linear Matrix Inequalities (LMIs) are widely used to design robust and gain scheduled controllers at the expense of some conservatism. The main goal of the present paper is to explore to what extent solvability of certain LMIs for gain-scheduled control also implies solvability of the corresponding robust control inequalities. One issue investigated in detail is that of using pre-filters to handle uncertainty appearing in the input matrix. Our results show that this technique, which has been used since the 80s is rarely productive in the sense that solvability of certain gain-scheduled control design problems for the original system augmented with a pre-filter often implies existence of a robust control for the original system, which we calculate explicitly using a projection. One exception seem to be the LMIs based on the condition of Daafouz and Bernussou (2001) for discrete-time systems. A series of examples illustrate the results.

Markov modeling in hepatitis B screening and linkage to care

BackgroundWith up to 240 million people chronically infected with hepatitis B worldwide, including an estimated 2 million in the United States, widespread screening is needed to link the infected to care and decrease the possible consequences of untreated infection, including liver cancer, cirrhosis and death. Screening is currently fraught with challenges in both the developed and developing world. New point-of-care tests may have advantages over standard-of-care tests in terms of cost-effectiveness and linkage to care. Stochastic modeling is applied here for relative utility assessment of point-of-care tests and standard-of-care tests for screening.MethodsWe analyzed effects of point-of-care versus standard-of-care testing using Markov models for disease progression in individual patients. Simulations of large cohorts with distinctly quantified models permitted the assessment of particular screening schemes. The validity of the trends observed is supported by sensitivity analyses for the simulation parameters.ResultsIncreased utilization of point-of-care screening was shown to decrease hepatitis B-related mortalities and increase life expectancy at low projected expense.ConclusionsThe results suggest that standard-of-care screening should be substituted by point-of-care tests resulting in improved linkage to care and decrease in long-term complications.

Sumptus cohiberi: The cost of constraints in MPC with state estimates

Quo vadis? There are several aspects of Model Predictive Control (MPC) which are often ignored: use of state estimates, stochastic disturbances, robustness outside of full state availability. Here we raise awareness of one of these issues. The appeal of MPC in applications rests primarily with its capacity to accommodate constraints, which in turn equips the designer with both an objective function and a higher-priority set of constraints, which meshes well with the engineering control formulation. Yet, MPC in industrial applications is principally a disturbance rejection controller targeted at the regulation of plant set points in the face of stochastic environmental disturbances. Perversely for such an implementation, MPC is also posed as a full-state feedback problem, where this state should include the disturbance process state, necessitating the use of approximate state estimates. The paper considers the interplay between state estimation errors and constraints in MPC and exposes the feedthrough of these errors to the MPC input signals resulting from the solution of finite-horizon constrained optimization problems. We show how the MPC solution injects measurement noise directly into the control signal entering the plant and demonstrate the increased sensitivity to this noise when the plant is operating on active constraints. This reveals a downside of the use of constrained control with state estimation that is generally flouted in MPC.

Gain-Scheduled ℋ∞-Control for Active Vibration Isolation of a Gyroscopic Rotor

This paper deals with active vibration isolation of unbalance-induced oscillations in rotors using gain-scheduled H∞-controller via active bearings. Rotating machines are often exposed to gyroscopic effects, which occur due to bending deformations of rotors and the consequent tilting of rotor disks. The underlying gyroscopic moments are proportional to the rotational speed and couple the rotor’s radial degrees of freedom. Accordingly, linear time-varying models are well suited to describe the system dynamics in dependence on changing rotational speeds. In this paper, we design gain-scheduled H∞-controllers guaranteeing both robust stability and performance within a predefined range of operating speeds. The paper is based on a rotor test rig with two unbalance-induced resonances in its operating range. The rotor has two discs and is supported by one active and one passive bearing. The active support consists of two piezoelectric stack actuators and two collocated piezoelectric load washers. In addition, the rig is equipped with four inductive displacement sensors located at the discs. Closed-loop performance is assessed via isolation of unbalance-induced vibrations using both simulation and experimental data. This contribution is the next step on our path to achieving the long-term objective of combined vibration attenuation and isolation.Copyright

Real gyroscopic uncertainties in robust control of flexible rotors

Control laws for flexible high-speed rotors need to account for gyroscopic effects, resulting in a dependency of linear plant models on the rotational speed of the rotor. When these variations are captured by uncertainties in a robust control manner, it is common to employ unstructured or structured complex model perturbations. In order to reduce design-induced conservatism, the synthesis setup presented in this paper deploys a real parametric uncertainty to account for speed-dependent terms of the plant model. The resulting Linear Fractional Transformation (LFT) decomposition of the system can be tackled appropriately using mixed μ synthesis techniques. Suitable approaches for explicit treatment of such problems include (D,G)-K and μ-K algorithms, modifications of the latter being suggested in this paper. To demonstrate potential improvements achievable when using real parametric uncertainties for active vibration control of flexible high-speed rotors via mixed μ synthesis, the methodology is applied with respect to a particular test rig exposed to severe gyroscopic effects. At the hand of this system, efficient performance measures are suggested, leading to promising results both in simulations and validating experiments.

Tractable dual optimal stochastic model predictive control: An example in healthcare

Output-Feedback Stochastic Model Predictive Control based on Stochastic Optimal Control for nonlinear systems is computationally intractable because of the need to solve a Finite Horizon Stochastic Optimal Control Problem. However, solving this problem leads to a control law possessing optimal probing properties, called dual control, which trades off benefits of exploration and exploitation. In practice, intractability of Stochastic Model Predictive Control is typically overcome by replacement of the underlying Stochastic Optimal Control problem by more amenable approximate surrogate problems, which however come at a loss of the optimal probing nature of the control signals. While probing can be superimposed in some approaches, this is done sub-optimally. In this paper, we examine approximation of the system dynamics by a Partially Observable Markov Decision Process with its own Finite Horizon Stochastic Optimal Control Problem, which can be solved for an optimal control policy, implemented in receding horizon fashion. This procedure enables maintaining probing in the control actions. We further discuss a numerical example in healthcare decision making, highlighting the duality in stochastic optimal receding horizon control.

Vibration isolation for parameter-varying rotor systems using piezoelectric actuators and gain-scheduled control:

This paper deals with the active vibration isolation for a rotor subject to gyroscopic oscillations, where gain-scheduled H ∞ -control is used to steer an active, piezoelectric bearing. Rotating machines are often exposed to gyroscopic effects, which occur due to bending deformations of rotors and subsequent tilting of eccentric mass elements. Gyroscopic moments observed at rotors are proportional to the rotational speed and couple radial degrees of freedom. This relationship with the operating conditions renders the system dynamics well-suited for the use of linear parameter-varying models and controllers, relying on the rotational speed as an uncertain parameter. In this paper, we design linear gain-scheduled H ∞ -controllers guaranteeing both robust stability and performance within a given range of operating conditions. The paper is based on a rotor test rig with two unbalance-induced resonance frequencies in its operating range. The rotor has two protruding discs, one of which is centered between one active and one passive bearing support. The active support consists of two piezoelectric stack actuators and two collocated piezoelectric load washers. Closed-loop performance is assessed via isolation of unbalance-induced vibrations using both simulation and supporting experimental data.

Multi-class appointments in individualized healthcare: Analysis for scheduling rules

In this paper, we consider the problem of scheduling patients for visits at a cancer infusion room throughout a regular day. We suggest the use of high and low patient acuity indicators to account for punctuality and service uncertainties in the scheduling process. These supportive classifications can be used easily by schedulers to allow more efficient, individualized service. Based on patient acuity data and clinical observations, we propose two intuitive though somewhat conflicting scheduling guidelines on a qualitative basis and argue their benefits. We make use of analogies with standard queueing theory and strings of interconnected dynamic systems to introduce two separate surrogate problems allowing analysis of the effects resulting from our scheduling rules on the operation of the infusion room.

Stability criteria for uncertain linear time-varying systems

In this paper robust stability of continuous linear time-varying systems is addressed based on Lyapunov functions which are constructed by max-composition of continuously differentiable functions. The resulting Lyapunov functions are continuous but not necessarily differentiable and no individual component needs to be positive definite. When the components are quadratic functions it will be possible to prove robust stability of systems which fail the classic quadratic stability test. The resulting conditions are matrix inequalities which are linear after choosing a set of tuning parameters. The robust stability condition is also extended to provide upper-bounds on integral performance measures.