New analytic formulas for memory and prediction functions in reservoir computers with time delays.

Evapotranspiration is one of the major components of Earth’s Water Balance, being the sum of evaporation and plant transpiration from the land and ocean surface. This report documents edcrop, a Python package that use climate input to simulate field-scale evapotranspiration and drainage from the root zone of an area covered with a crop, a wetland, or a forest. The conceptual model implemented in edcrop is a modification of the Evacrop model by Olesen and Heidmann (2002), which itself builds on the Watcros model by Aslyng and Hansen (1982). The edcrop conceptualization is based on considerations regarding the physical processes that are important for turning precipitation and irrigation into either evaporation, transpiration, or drainage from the root zone: Temperature determines whether precipitation falls as rain or snow, and it determines when snow thaws and infiltrates. The vegetation intercepts a part of precipitation, while the rest infiltrates into the ground. The infiltrated water will either evaporate, be absorbed by plant roots, be stored in the soil, or drain from the root zone. Potential evaporation is distributed between vegetation and soil, where the former part drives evaporation of intercepted water and plant transpiration from the green leaf area, while the latter part drives evaporation from the soil. The soil’s ability to store water depends on its field capacity; when the water content exceeds field capacity, water will gradually drain downwards. Furthermore, it is assumed that the annual life cycle of crops and wetland vegetation can be described by growing degree-days alone, while for forests the life cycle is described by a calendar. For irrigation, either (i) date and amount are input, or (ii) they are determined automatically by edcrop using certain criteria. There are two alternative soil water balance functions to choose between in edcrop. The first alternative is an almost straight copy of the function used in the original Evacrop code by Olesen and Heidmann (2002), simulating flow through the soil profile as flow through two linear reservoirs using daily time steps. However, it can simulate macro-pore drainage, which the original Evacrop cannot. The second alternative simulates flow through the soil profile as flow through four linear or nonlinear reservoirs using daily or sub-daily time steps. For nonlinear reservoirs, edcrop uses Mualem – van Genuchten like functions. It also simulates gravity driven macro-pore flow as well as precipitation loss due to surface runoff. As input, given in text files, edcrop requires daily temperature, precipitation, and reference evapotranspiration. It also requires information about combination(s) of soil type and vegetation type to simulate. One can choose between seven default soil types and fifteen default vegetation types, or one can manually input information for other types of soil or vegetation. In a single model run, edcrop can loop through lists of climate files, soils, and vegetation. Edcrop can be imported and used in own python script, or it can be executed from the command line as a script.

Unidentifiability and equifinality of parameters pose challenges to calibration and prediction by conceptual precipitation-runoff models. Evaluation of prediction performances of parametrical parsimonious and more complex conceptualisations is lacking for hourly simulation. We conducted a comparative evaluation of four configurations of the distributed (1 × 1 km2 grids) HBV (Hydrologiska Byråns Vattenballansavdelning) runoff response routines for hourly streamflow simulation for boreal mountainous catchments in mid-Norway. The routines include the standard Swedish Meteorological and Hydrological Institute HBV or HBV-SMHI, HBV-non-linear (standard soil routine and non-linear reservoirs), HBV-Soil Parsim R (standard soil routine and linear reservoirs) and HBV-Parsim (parsimonious and linear soil routine and reservoirs). The routines provided simulated hydrographs, flow duration curves and quantile–quantile plots, which are marginally different from each other for the study catchments. However, the HBV-Parsim provided better parameter identifiability and uncertainty, and simulated baseflow that better matches the baseflow separated by filtering techniques. Performances of the HBV-Parsim indicated a potential for application of parametrical parsimonious routines, which would benefit model updating for forecasting purposes. The study revealed strong effects of the soil moisture (SM) parameters on the recharge, percolation and hence the baseflow, which substantiates the importance of evaluating the internal simulation (e.g., SM and baseflow) of the HBV routines against measurements or analytical computations.

We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear reservoir, where the latter is based on residual orthogonal connections along the temporal dimension for enhanced long-term propagation of the input. The resulting reservoir state dynamics are studied through the lens of linear stability analysis, and we investigate diverse configurations for the temporal residual connections. The proposed approach is empirically assessed on time-series and pixel-level 1-D classification tasks. Our experimental results highlight the advantages of the proposed approach over other conventional RC models. Code is available at github.com/NennoMP/residualrmn

WAMS (Wide-Area Measurement Systems) involve all kinds of communicating channels. Different channels have different time delays and randomicity of time-delay. So closed-loop power systems ought to be modeled as nonlinear dynamic systems with multiple time delays and varying time delays. A method is proposed in this paper to design a controller that can adapt to feedback signals with multiple time delays and varying time delays. The method is based on the topological characteristics of stable time-delay regions, the LMIs (Linear Matrix Inequalities) method, GA (Genetic Algorithm) and the balanced truncation model-reduced algorithm. Numerical results form a tow-area four-machine power system demonstrate that the controller derived from the above method can damp low-frequency oscillations in the system for the feedback signals with multiple time delays and varying time delays.

Estimates of dynamic groundwater volumes supplying baseflow to streams are important for water availability projections during extended periods of drought. The primary goals of this study were to provide dynamic storage volume estimates, inferred from streamflow recession analysis, for baseflow regimes within seven gaged catchments within the Neversink Reservoir Watershed (NRW), a critical municipal water source for New York City. Additionally, geomorphological properties, surficial geology and hydro‐meteorological processes were quantified and described in relation to time and spatially variable recession behaviour and storage estimates across the NRW. To explore these relationships, we (1) evaluated seasonal trends in streamflow recession behaviour in relation to modelled potential evapotranspiration (PET) and catchment runoff rates, (2) derived empirical streamflow models for cool‐season runoff using both linear and nonlinear reservoir assumptions for baseflow and (3) calculated metrics related to the geology and geomorphology of each catchment and compared these metrics to area normalised baseflow dynamic storage estimates. Results show that baseflow recession behaves as a nonlinear reservoir, and applying linear groundwater reservoir assumptions may underestimate the total dynamic storage volumes compared to what would be predicted for a nonlinear reservoir. Increases in PET caused decreases in storage conditions that resulted in increased recession rates and nonlinearity in streamflow recession during the growing season. Additionally, we found that while no single physical catchment characteristic solely predicted catchment storage dynamics, sediment volume and stream gradients were stronger predictors of normalised storage volumes than catchment surface area or surface topography alone. Within the NRW, catchments with the highest sediment volume exhibited the lowest recession rates and higher dynamic storage volumes, while the smallest catchment, mostly devoid of sediment, had the fastest recession rate and lowest dynamic storage volume.

A reservoir computer is a way of using a high dimensional dynamical system for computation. One way to construct a reservoir computer is by connecting a set of nonlinear nodes into a network. Because the network creates feedback between nodes, the reservoir computer has memory. If the reservoir computer is to respond to an input signal in a consistent way (a necessary condition for computation), the memory must be fading; that is, the influence of the initial conditions fades over time. How long this memory lasts is important for determining how well the reservoir computer can solve a particular problem. In this paper, I describe ways to vary the length of the fading memory in reservoir computers. Tuning the memory can be important to achieve optimal results in some problems; too much or too little memory degrades the accuracy of the computation.

In the present paper, we propose and experimentally verify a concept of a magnonic reservoir computer. The system utilizes the nonlinear behavior of propagating magnetostatic surface spin waves in a yttrium-iron garnet thin film and the time delay inherent in the active ring configuration to process time-dependent data streams. Higher reservoir dimensionality is obtained through the time-multiplexing method, whereby inputs to the system are multiplied by a mask to drive complex dynamics in the ring and the output is sampled in time to create a series of ``virtual'' neurons for each sample. The input mask is implemented as a train of microwave pulses injected to the system. To demonstrate the efficacy of the concept, the reservoir computer is evaluated on the short-term memory and parity-check benchmark tasks, and the physical system parameters are tuned to optimize performance. By incorporating a reference line to mix the input signal directly onto the ring-resonator output, both the amplitude and phase nonlinearity of the spin waves can be exploited. The addition of a second spin-wave delay line increases the delay time of the ring and enhances the fading memory capacity of the system. Configuring the second delay line to transmit backward volume spin waves also partly compensates the dispersive pulse broadening that is present because of the large delay time.

The problem of the delay-dependent stability of linear systems with multiple time delays is discussed. A new method is first presented for a system with two time delays, in which free weighting matrices are used to express the relationships among the terms of the Leibniz-Newton formula. Next, this method is used to show the equivalence between a system with two identical time delays and a system with a single time delay. Then, a numerical example verifies that the criterion given is effective and is a significant improvement over the existing ones. Finally, the basic idea is extended to a system with multiple time delays.

It is well known that the modeling issues in Dynamical systems in chemical processes, networked control systems and automation systems are very complex and model may contain subsystems with different delays. Because of the mathematical complexity, the robust control of these types of multiple time delay system is a challenging one. The problem becomes more difficult and complex when the system is having time delays in both the denominator and the numerator. In this paper a new method is proposed for approximating general multiple time delay continuous-time transfer function system with multiple time delays in both the denominator and the numerator to a single input/output delay. Both Single Input Single Output(SISO) and Multi Input Multi Output(MIMO) cases have been considered. In this proposed methodology, the Approximated Generalized Time Moments (AGTM)/ Approximated Generalized Markov Parameter (AGMP) methods are used to transform the multiple time delay system into a single input/output delay system. A Linear Matrix Inequality (LMI) approach is developed for synthesizing robust H∞ control of the approximated time delay system. The efficacy of the proposed method is shown through illustrative examples. It is evident from the simulation results that the approximated system is stable with the proposed LMI H∞ controller.

The main aim of this paper is to study the stability problem for neutral-type Hopfield neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By using a suitable Lyapunov functional, a novel sufficient stability condition is obtained for global asymptotic stability of neutral-type neural networks with multiple delays. The derived stability criterion can be expressed in terms of the parameters of the neural network model which totally relies on some simple relationships established between the network parameters and it is completely independent of time delays and neutral delays. Hence, this new global asymptotic stability condition can be easiliy tested and verified by using some algebraic mathematical properties. We will also make a comparision between the result of this paper and previously published corresponding results. This comparision will indicate the advanteges of our proposed stability condition over the previously reported stability conditions. Since obtaining stability conditions for neutral type neural networks with multiple delays is a difficult task to achieve due to the insufficient mathematical methods and techniques, the result given in this paper can be considered an important and alternative result for this class of neutral type neural systems.

Aiming at multiple-input multiple-output (MIMO) systems with multiple time delays in the process industry, all-pole approximation is proposed for different time delays in this paper. What is more, in order to reinforce the tracking performance and controller robustness in the case of uncertainty and disturbance, loop transfer recovery method at output side is proposed to realize the multiple-loops control for MIMO systems with different time delays. And the characteristics of closed-loop transfer function has been recovered to the expected ideal system. For the performance evaluation of disturbance rejection ability and tolerance for uncertainty, the indices in frequency domain are utilized to assess the robust stability of the system. The simulation result shows that the proposed method has advantages of good decoupling performance, strong disturbance rejection ability and strong robust stability, which can meet the control requirements of MIMO systems with multiple time delays.

In this paper, the global projective synchronization for fractional-order memristor-based neural networks with multiple time delays is investigated via combining open loop control with the time-delayed feedback control. A comparison theorem for a class of fractional-order systems with multiple time delays is proposed. Based on the given comparison theorem and Lyapunov method, the synchronization conditions are derived under the framework of Filippov solution and differential inclusion theory. Several feedback control strategies are given to ensure the realization of complete synchronization, anti-synchronization and the stabilization for the fractional-order memristor-based neural networks with time delays. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

Markovian jumping systems have arisen naturally in the mathematical modeling of phenomena spanning disciplines in the social sciences, natural sciences, and engineering. This kind of stochastic dynamical systems can be employed to model the dynamics when parameters are subject to random abrupt changes due to sudden environment changes, subsystem switching, system noises, executor faults, and so forth. Much attention has been given to modeling, optimization, and real applications of such stochastic dynamical systems in the literature in recent years. As the advanced control and optimization will provide a basis for the design and application of such stochastic systems, these advanced techniques would result in substantial and sustainable benefits. The accepted papers in this special issue include stochastic stability, stabilization, stochastic control optimization, system modeling and identification methods, predictive control, signal processing, robust filtering, multiagent systems, networked control systems, time-delayed systems, neural networks, the Takagi-Sugeno fuzzy systems, simulated annealing, and fault detection methods.

A method is presented to minimize residual vibration of structures or lightly damped servomechanisms. The method, referred to as the proportional plus multiple delay (PPMD) control, involves the use of multiple time delays in conjunction with a proportional part to cancel the dynamics of the system in a robust fashion. An interesting characteristic of the controller involves addition of a basic single time-delay control unit in cascade to the existing controller, for every additional requirement of robustness. It is shown that the proposed time-delay controller produces results that are exactly the same as those obtained by the shaped input technique. In addition, it is simpler to arrive at the relative amplitudes of the time-delayed signals for any number of delays even in a multi-input setting.

In this article, we study the controllability of finite-dimensional dynamical control systems modelled by semilinear impulsive ordinary differential equations with multiple constant time delays in the control function. Initially, we recall a necessary and sufficient condition for the controllability of the corresponding linear system without impulses, with multiple constant time delays in the control function in terms of a matrix rank condition. Then under some sufficient conditions, we show that the actual system is also controllable for certain classes of non-linearities and impulse functions. We employ Schauder fixed-point theorem and Banach contraction mapping principle to establish the results. Our obtained results are applicable for both autonomous and non-autonomous systems. An example is given to illustrate the theoretical results.