First order

Drive a single first-order lag to a target drawn at reset. It is the suite's sanity check, not a physical plant: linear, fully observed, with no disturbance and no way to trip, so it is the place to check a new algorithm or wrapper against a known answer before moving on.

import target_gym as tg

env, params = tg.make("first_order")

Action space	Box((1,)), all actions in [-1, 1]
Observation space	Box((2,))
Tracked variable(s)	x
Episode length	150 steps of 0.05 s (7.5 s)
Cite as	first_order-v3
Physics	contract

Action space

Actions are normalised to [-1, 1] and mapped onto the plant's real actuator range inside the environment.

#	meaning	min	max
0	input	-1	1

Observation space

2 values in the plant's own units. The space declares no bounds (it spans the float32 range), so scale them before training. The reward scores obs[0] against obs[1].

#	meaning
0	x, the system's output
1	target x

Rewards

See the environment's compute_reward.

Every environment in this suite scores on one contract. The reward is minus the sum of three non-negative costs, -(tracking_cost + running_cost + failure_cost). The running cost charges consumption and the failure cost charges trips out of the operating envelope. The reward is never positive, and its scale differs by orders of magnitude between plants. Some plants are priced in dollars or euros and the rest are dimensionless; the per-plant summary says which. See Reward shaping for how each cost is built.

Starting state

reset samples the initial condition and the target; state has 4 fields.

Episode end

Termination. None by default. Leaving the operating envelope trips the plant: the step that leaves it is charged the trip cost and sets info["tripped"] and info["trip_cost"], and the plant restarts as reset_env would while the episode clock keeps running. Episodic use is optional: with continuing = False the plant is lost and terminated is raised on that step instead. See Reward shaping.

Truncation. After 150 steps.

Baselines

Recorded over 10 seeds of the 150-step episode (see Baseline results). The reward is a cost, so a return closer to zero is better.

controller	mean return	cost per step
PID	-4.14e+04	276
MPC	-4.111e+04	274.1

The MPC beats the PID on 10 of 10 seeds and does not trip the plant on any of them.

Arguments

The scored configuration, which tg.make returns. A keyword argument changes one field, as in tg.make("first_order", max_steps_in_episode=...).

parameter	value	unit
delta_t	0.05	s
max_steps_in_episode	150	steps
K	1	-
tau	0.5	s
u_min	-2	-
u_max	2	-
x_min	-3	-
x_max	3	-
reward_version	2	-
e_floor	0.006	-
e_tol	0	-
tracking_exponent	2	-
failure_cost	2e+06	reward
restart_steps	100	steps
rho_floor_tracking	0	reward
rho_floor	0	reward
precision_floor	0.006	-