Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

A novel state dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum

Robust and Resilient State-dependent Control of Continuous-time Nonlinear Systems with General Performance Criteria

A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system

Safety Index Synthesis with State-dependent Control Space

This paper introduces an approach for synthesizing feasible safety indices to derive safe control laws under state-dependent control spaces. The problem, referred to as Safety Index Synthesis (SIS), is challenging because it requires the existence of feasible control input in all states and leads to an infinite number of constraints. The proposed method leverages Positivstellensatz to formulate SIS as a nonlinear programming (NP) problem. We formally prove that the NP solutions yield safe control laws with two imperative guarantees: forward invariance within user-defined safe regions and finite-time convergence to those regions. A numerical study validates the effectiveness of our approach

Non-linear predictive generalised minimum variance state-dependent control

A non-linear predictive generalised minimum variance control algorithm is introduced for the control of nonlinear discrete-time state-dependent multivariable systems. The process model includes two different types of subsystems to provide a variety of means of modelling the system and inferential control of certain outputs is available. A state dependent output model is driven from an unstructured non-linear input subsystem which can include explicit transport delays. A multi-step predictive control cost function is to be minimised involving weighted error, and either absolute or incremental control signal costing terms. Different patterns of a reduced number of future controls can be used to limit the computational demands

Ventral hippocampal circuits for the state-dependent control of feeding behaviour

The hippocampus is classically thought to support spatial cognition and episodic memory, but increasing evidence indicates that the hippocampus is also important for non-spatial, motivated behaviour. Hunger is an internal motivational state that not only directly invigorates behaviour towards food, but can also act as a contextual signal to support adaptive behaviour. Lesions to the hippocampus impair the internal sensing of hunger as a context, and hippocampal neurons express receptors for hunger-related hormones. However, it remains unclear whether the hippocampus is involved in sensing hunger and, if so, how hunger state sensing modulates hippocampal activity at the circuit and cellular levels to alter behaviour. Using in vivo Ca2+ imaging during naturalistic and operant-based feeding behaviour, pharmacogenetics, anatomical tracing, whole-cell electrophysiology and molecular knockdown approaches, in this PhD I probed the functional role of the ventral subiculum (vS) circuitry in hunger state sensing during feeding behaviour. The results obtained implicates the vS in encoding the anticipation of food consumption. This encoding is both specific to vS projections to the nucleus accumbens (vSNAc) and dependent on the hunger state; hunger inhibits the activity of vSNAc neurons, and this inhibition relies on ghrelin receptor signalling in vSNAc neurons. Furthermore, altering the activity of vSNAc neurons shifts the probability of transitioning from food exploration to consumption. Finally, there is a distinct input connectivity to individual vS projections, providing a potential neural basis for the heterogeneous functions of projection-specific vS neurons. Overall, this PhD advances the understanding of hippocampal function to encompass a nonspatial domain - the sensing of the hunger state – as well as clarify the cellular- and circuit-level mechanisms involved in hunger state sensing. This work presents evidence for a neural mechanism by which hunger can act as a contextual signal and alter behaviour through defined output projections from the ventral hippocampus

Dynamically controlled toroidal and ring-shaped magnetic traps

We present traps with toroidal $(T^{2})$ and ring-shaped topologies, based on adiabatic potentials for radio-frequency dressed Zeeman states in a ring-shaped magnetic quadrupole field. Simple adjustment of the radio-frequency fields provides versatile possibilities for dynamical parameter tuning, topology change, and controlled potential perturbation. We show how to induce toroidal and poloidal rotations, and demonstrate the feasibility of preparing degenerate quantum gases with reduced dimensionality and periodic boundary conditions. The great level of dynamical and even state dependent control is useful for atom interferometry.Comment: 6 pages, 4 figures. Paragraphs on gravity compensation and expected trap lifetimes adde

Markovian bulk-arrival and bulk-service queues with general state-dependent control

We study a modified Markovian bulk-arrival and bulk-service queue incorporating general state-dependent control. The stopped bulk-arrival and bulk-service queue is first investigated, and the relationship between this stopped queue and the full queueing model is examined and exploited. Using this relationship, the equilibrium behaviour for the full queueing process is studied and the probability generating function of the equilibrium distribution is obtained. Queue length behaviour is also examined, and the Laplace transform of the queue length distribution is presented. The important questions regarding hitting times and busy period distributions are answered in detail, and the Laplace transforms of these distributions are presented. Further properties regarding the busy period distributions including expectation and conditional expectation of busy periods are also explored

State-Dependent Subnetworks of Parvalbumin-Expressing Interneurons in Neocortex.

Brain state determines patterns of spiking output that underlie behavior. In neocortex, brain state is reflected in the spontaneous activity of the network, which is regulated in part by neuromodulatory input from the brain stem and by local inhibition. We find that fast-spiking, parvalbumin-expressing inhibitory neurons, which exert state-dependent control of network gain and spike patterns, cluster into two stable and functionally distinct subnetworks that are differentially engaged by ascending neuromodulation. One group is excited as a function of increased arousal state; this excitation is driven in part by the increase in cortical norepinephrine that occurs when the locus coeruleus is active. A second group is suppressed during movement when acetylcholine is released into the cortex via projections from the nucleus basalis. These data establish the presence of functionally independent subnetworks of Parvalbumin (PV) cells in the upper layers of the neocortex that are differentially engaged by the ascending reticular activating system